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On the design space between molecular mechanics and machine learning force fields (2409.01931v2)

Published 3 Sep 2024 in physics.chem-ph, cs.AI, cs.LG, physics.bio-ph, and physics.comp-ph

Abstract: A force field as accurate as quantum mechanics (QM) and as fast as molecular mechanics (MM), with which one can simulate a biomolecular system efficiently enough and meaningfully enough to get quantitative insights, is among the most ardent dreams of biophysicists -- a dream, nevertheless, not to be fulfilled any time soon. Machine learning force fields (MLFFs) represent a meaningful endeavor towards this direction, where differentiable neural functions are parametrized to fit ab initio energies, and furthermore forces through automatic differentiation. We argue that, as of now, the utility of the MLFF models is no longer bottlenecked by accuracy but primarily by their speed (as well as stability and generalizability), as many recent variants, on limited chemical spaces, have long surpassed the chemical accuracy of $1$ kcal/mol -- the empirical threshold beyond which realistic chemical predictions are possible -- though still magnitudes slower than MM. Hoping to kindle explorations and designs of faster, albeit perhaps slightly less accurate MLFFs, in this review, we focus our attention on the design space (the speed-accuracy tradeoff) between MM and ML force fields. After a brief review of the building blocks of force fields of either kind, we discuss the desired properties and challenges now faced by the force field development community, survey the efforts to make MM force fields more accurate and ML force fields faster, envision what the next generation of MLFF might look like.

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References (297)
  1. L. Boltzmann, “Studien uber das gleichgewicht der lebenden kraft,” Wissenschafiliche Abhandlungen 1, 49–96 (1868).
  2. J. A. McCammon, B. R. Gelin,  and M. Karplus, “Dynamics of folded proteins,” nature 267, 585–590 (1977).
  3. J. W. Ponder and D. A. Case, “Force fields for protein simulations,” in Advances in protein chemistry, Vol. 66 (Elsevier, 2003) pp. 27–85.
  4. D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark,  and H. J. Berendsen, “Gromacs: fast, flexible, and free,” Journal of computational chemistry 26, 1701–1718 (2005).
  5. D. A. Case, T. E. Cheatham III, T. Darden, H. Gohlke, R. Luo, K. M. Merz Jr, A. Onufriev, C. Simmerling, B. Wang,  and R. J. Woods, “The amber biomolecular simulation programs,” Journal of computational chemistry 26, 1668–1688 (2005).
  6. J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kale,  and K. Schulten, “Scalable molecular dynamics with namd,” Journal of computational chemistry 26, 1781–1802 (2005).
  7. F. E. Calculations, “Theory and applications in chemistry and biology,” Springer Series in Chemical Physics 86 (2007).
  8. C. Wang, G. Pilania, S. Boggs, S. Kumar, C. Breneman,  and R. Ramprasad, “Computational strategies for polymer dielectrics design,” Polymer 55, 979 – 988 (2014).
  9. C. Li and A. Strachan, “Molecular scale simulations on thermoset polymers: A review,” Journal of Polymer Science Part B: Polymer Physics 53, 103–122 (2015).
  10. H. Sun, Z. Jin, C. Yang, R. L. Akkermans, S. H. Robertson, N. A. Spenley, S. Miller,  and S. M. Todd, “Compass ii: extended coverage for polymer and drug-like molecule databases,” Journal of molecular modeling 22, 47 (2016).
  11. M. J. Harvey, G. Giupponi,  and G. D. Fabritiis, “Acemd: accelerating biomolecular dynamics in the microsecond time scale,” Journal of chemical theory and computation 5, 1632–1639 (2009).
  12. R. Salomon-Ferrer, A. W. Gotz, D. Poole, S. Le Grand,  and R. C. Walker, “Routine microsecond molecular dynamics simulations with amber on gpus. 2. explicit solvent particle mesh ewald,” Journal of chemical theory and computation 9, 3878–3888 (2013).
  13. P. Eastman, J. Swails, J. D. Chodera, R. T. McGibbon, Y. Zhao, K. A. Beauchamp, L.-P. Wang, A. C. Simmonett, M. P. Harrigan, C. D. Stern, et al., “Openmm 7: Rapid development of high performance algorithms for molecular dynamics,” PLoS computational biology 13, e1005659 (2017).
  14. P. Eastman, R. Galvelis, R. P. Peláez, C. R. A. Abreu, S. E. Farr, E. Gallicchio, A. Gorenko, M. M. Henry, F. Hu, J. Huang, A. Krämer, J. Michel, J. A. Mitchell, V. S. Pande, J. P. Rodrigues, J. Rodriguez-Guerra, A. C. Simmonett, S. Singh, J. Swails, P. Turner, Y. Wang, I. Zhang, J. D. Chodera, G. D. Fabritiis,  and T. E. Markland, “Openmm 8: Molecular dynamics simulation with machine learning potentials,”  (2023a), arXiv:2310.03121 [physics.chem-ph] .
  15. L. Wang, Y. Wu, Y. Deng, B. Kim, L. Pierce, G. Krilov, D. Lupyan, S. Robinson, M. K. Dahlgren, J. Greenwood, et al., “Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field,” Journal of the American Chemical Society 137, 2695–2703 (2015).
  16. C. E. Schindler, H. Baumann, A. Blum, D. Bose, H.-P. Buchstaller, L. Burgdorf, D. Cappel, E. Chekler, P. Czodrowski, D. Dorsch, et al., “Large-scale assessment of binding free energy calculations in active drug discovery projects,” Journal of Chemical Information and Modeling 60, 5457–5474 (2020).
  17. V. Gapsys, D. F. Hahn, G. Tresadern, D. L. Mobley, M. Rampp,  and B. L. de Groot, “Pre-exascale computing of protein–ligand binding free energies with open source software for drug design,” Journal of chemical information and modeling 62, 1172–1177 (2022).
  18. S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. T. Schütt,  and K.-R. Müller, “Machine learning of accurate energy-conserving molecular force fields,” Science advances 3, e1603015 (2017a).
  19. S. Boothroyd, P. K. Behara, O. C. Madin, D. F. Hahn, H. Jang, V. Gapsys, J. R. Wagner, J. T. Horton, D. L. Dotson, M. W. Thompson, et al., “Development and benchmarking of open force field 2.0.0: The sage small molecule force field,” Journal of Chemical Theory and Computation , 3251––3275 (2023).
  20. K. Takaba, A. J. Friedman, C. E. Cavender, P. K. Behara, I. Pulido, M. M. Henry, H. MacDermott-Opeskin, C. R. Iacovella, A. M. Nagle, A. M. Payne, M. R. Shirts, D. L. Mobley, J. D. Chodera,  and Y. Wang, “Machine-learned molecular mechanics force fields from large-scale quantum chemical data,” Chem. Sci. 15, 12861–12878 (2024).
  21. S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. T. Schütt,  and K.-R. Müller, “Machine learning of accurate energy-conserving molecular force fields,” Science Advances 3, e1603015 (2017b).
  22. O. T. Unke, S. Chmiela, H. E. Sauceda, M. Gastegger, I. Poltavsky, K. T. Schütt, A. Tkatchenko,  and K.-R. Müller, “Machine learning force fields,” Chemical Reviews 121, 10142–10186 (2021).
  23. J. S. Smith, O. Isayev,  and A. E. Roitberg, “Ani-1: an extensible neural network potential with dft accuracy at force field computational cost,” Chemical science 8, 3192–3203 (2017a).
  24. J. S. Smith, B. Nebgen, N. Lubbers, O. Isayev,  and A. E. Roitberg, “Less is more: Sampling chemical space with active learning,” The Journal of chemical physics 148, 241733 (2018).
  25. J. S. Smith, B. T. Nebgen, R. Zubatyuk, N. Lubbers, C. Devereux, K. Barros, S. Tretiak, O. Isayev,  and A. E. Roitberg, “Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning,” Nature communications 10, 1–8 (2019).
  26. C. Devereux, J. S. Smith, K. K. Davis, K. Barros, R. Zubatyuk, O. Isayev,  and A. E. Roitberg, “Extending the applicability of the ani deep learning molecular potential to sulfur and halogens,” Journal of Chemical Theory and Computation 16, 4192–4202 (2020).
  27. K. T. Schütt, H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko,  and K.-R. Müller, “Schnet–a deep learning architecture for molecules and materials,” The Journal of Chemical Physics 148, 241722 (2018).
  28. S. Batzner, T. E. Smidt, L. Sun, J. P. Mailoa, M. Kornbluth, N. Molinari,  and B. Kozinsky, “Se (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials,” arXiv preprint arXiv:2101.03164  (2021).
  29. Y. Han, Z. Wang, Z. Wei, J. Liu,  and J. Li, “Machine learning builds full-QM precision protein force fields in seconds,” Briefings in Bioinformatics 22 (2021), 10.1093/bib/bbab158, bbab158, https://academic.oup.com/bib/article-pdf/22/6/bbab158/41089104/bbab158.pdf .
  30. Y. Wang and J. D. Chodera, “Spatial attention kinetic networks with e(n)-equivariance,”  (2023), arXiv:2301.08893 [cs.LG] .
  31. A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. J. Owen, M. Kornbluth,  and B. Kozinsky, “Learning local equivariant representations for large-scale atomistic dynamics,”  (2022), arXiv:2204.05249 [physics.comp-ph] .
  32. G. D. Fabritiis, “Machine learning potentials: A roadmap toward next-generation biomolecular simulations,”  (2024), arXiv:2408.12625 [physics.chem-ph] .
  33. S. Barnett and J. D. Chodera, “Neural network potentials for enabling advanced small-molecule drug discovery and generative design,” GEN Biotechnology 3, 119–129 (2024).
  34. J. Behler and M. Parrinello, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Phys. Rev. Lett. 98, 146401 (2007).
  35. S. Thais and D. Murnane, “Equivariance is not all you need: Characterizing the utility of equivariant graph neural networks for particle physics tasks,”  (2023), arXiv:2311.03094 [cs.LG] .
  36. O. Puny, M. Atzmon, H. Ben-Hamu, I. Misra, A. Grover, E. J. Smith,  and Y. Lipman, “Frame averaging for invariant and equivariant network design,”  (2022), arXiv:2110.03336 [cs.LG] .
  37. A. Duval, V. Schmidt, A. H. Garcia, S. Miret, F. D. Malliaros, Y. Bengio,  and D. Rolnick, “Faenet: Frame averaging equivariant gnn for materials modeling,”  (2023), arXiv:2305.05577 [cs.LG] .
  38. J. A. Barker and R. O. Watts, “Monte carlo studies of the dielectric properties of water-like models,” Molecular Physics 26, 789–792 (1973).
  39. R. Watts, “Monte carlo studies of liquid water,” Molecular Physics 28, 1069–1083 (1974).
  40. D.-A. Clevert, T. Unterthiner,  and S. Hochreiter, “Fast and accurate deep network learning by exponential linear units (elus),”  (2016), arXiv:1511.07289 [cs.LG] .
  41. X. Fu, Z. Wu, W. Wang, T. Xie, S. Keten, R. Gomez-Bombarelli,  and T. Jaakkola, “Forces are not enough: Benchmark and critical evaluation for machine learning force fields with molecular simulations,”  (2023), arXiv:2210.07237 [physics.comp-ph] .
  42. S. Stocker, J. Gasteiger, F. Becker, S. Günnemann,  and J. T. Margraf, “How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?” Machine Learning: Science and Technology 3, 045010 (2022).
  43. W. Wang, T. Yang, W. H. Harris,  and R. Gómez-Bombarelli, “Active learning and neural network potentials accelerate molecular screening of ether-based solvate ionic liquids,” Chemical Communications 56, 8920–8923 (2020a).
  44. D. Schwalbe-Koda, A. R. Tan,  and R. Gómez-Bombarelli, “Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks,” Nature communications 12, 5104 (2021).
  45. K. Lindorff-Larsen, S. Piana, R. O. Dror,  and D. E. Shaw, “How fast-folding proteins fold,” Science 334, 517–520 (2011).
  46. J. Kubelka, J. Hofrichter,  and W. A. Eaton, “The protein folding ‘speed limit’,” Current opinion in structural biology 14, 76–88 (2004).
  47. W. A. Eaton, “Modern kinetics and mechanism of protein folding: A retrospective,” The Journal of Physical Chemistry B 125, 3452–3467 (2021).
  48. B. Manavalan, K. Kuwajima,  and J. Lee, “Pfdb: A standardized protein folding database with temperature correction,” Scientific reports 9, 1588 (2019).
  49. J.-C. Horng, V. Moroz,  and D. P. Raleigh, “Rapid cooperative two-state folding of a miniature α𝛼\alphaitalic_α–β𝛽\betaitalic_β protein and design of a thermostable variant,” Journal of molecular biology 326, 1261–1270 (2003).
  50. Z. Qiao, M. Welborn, A. Anandkumar, F. R. Manby,  and T. F. Miller, “Orbnet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital features,” The Journal of chemical physics 153 (2020).
  51. M. Retchin, Y. Wang, K. Takaba,  and J. D. Chodera, “Druggym: A testbed for the economics of autonomous drug discovery,” bioRxiv , 2024–05 (2024).
  52. A. G. Baydin, B. A. Pearlmutter, A. A. Radul,  and J. M. Siskind, “Automatic differentiation in machine learning: a survey,”  (2018), arXiv:1502.05767 [cs.SC] .
  53. J. A. Pople, “Nobel lecture: Quantum chemical models,” Reviews of Modern Physics 71, 1267 (1999).
  54. M. Bogojeski, L. Vogt-Maranto, M. E. Tuckerman, K.-R. Müller,  and K. Burke, “Quantum chemical accuracy from density functional approximations via machine learning,” Nature communications 11, 5223 (2020).
  55. D. L. Mobley and P. V. Klimovich, “Perspective: Alchemical free energy calculations for drug discovery,” The Journal of chemical physics 137 (2012).
  56. I. Batatia, D. P. Kovács, G. N. C. Simm, C. Ortner,  and G. Csányi, “Mace: Higher order equivariant message passing neural networks for fast and accurate force fields,”  (2023), arXiv:2206.07697 [stat.ML] .
  57. S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt,  and B. Kozinsky, “E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials,” Nature Communications 13 (2022), 10.1038/s41467-022-29939-5.
  58. A. S. Christensen and O. A. von Lilienfeld, “On the role of gradients for machine learning of molecular energies and forces,”  (2020a), arXiv:2007.09593 [physics.chem-ph] .
  59. P. Eastman, P. K. Behara, D. L. Dotson, R. Galvelis, J. E. Herr, J. T. Horton, Y. Mao, J. D. Chodera, B. P. Pritchard, Y. Wang, et al., “Spice, a dataset of drug-like molecules and peptides for training machine learning potentials,” Scientific Data 10, 11 (2023b).
  60. J. S. Smith, R. Zubatyuk, B. Nebgen, N. Lubbers, K. Barros, A. E. Roitberg, O. Isayev,  and S. Tretiak, “The ani-1ccx and ani-1x data sets, coupled-cluster and density functional theory properties for molecules,” Scientific data 7, 134 (2020).
  61. D. P. Kovács, J. H. Moore, N. J. Browning, I. Batatia, J. T. Horton, V. Kapil, W. C. Witt, I.-B. Magdău, D. J. Cole,  and G. Csányi, “Mace-off23: Transferable machine learning force fields for organic molecules,”  (2023a), arXiv:2312.15211 [physics.chem-ph] .
  62. G. Simeon and G. De Fabritiis, “Tensornet: Cartesian tensor representations for efficient learning of molecular potentials,” Advances in Neural Information Processing Systems 36 (2024).
  63. P. Dauber-Osguthorpe and A. T. Hagler, “Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there?” Journal of computer-aided molecular design 33, 133–203 (2019).
  64. A. T. Hagler, “Force field development phase ii: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics,” Journal of computer-aided molecular design 33, 205–264 (2019).
  65. C. Ringrose, J. T. Horton, L.-P. Wang,  and D. J. Cole, “Exploration and validation of force field design protocols through qm-to-mm mapping,” Physical Chemistry Chemical Physics 24, 17014–17027 (2022).
  66. X. C. Yan, M. J. Robertson, J. Tirado-Rives,  and W. L. Jorgensen, “Improved description of sulfur charge anisotropy in opls force fields: model development and parameterization,” The Journal of Physical Chemistry B 121, 6626–6636 (2017).
  67. M. H. Kolar and P. Hobza, “Computer modeling of halogen bonds and other σ𝜎\sigmaitalic_σ-hole interactions,” Chemical reviews 116, 5155–5187 (2016).
  68. J. Delhommelle and P. Millié, “Inadequacy of the lorentz-berthelot combining rules for accurate predictions of equilibrium properties by molecular simulation,” Molecular Physics 99, 619–625 (2001).
  69. T. A. Halgren, “The representation of van der waals (vdw) interactions in molecular mechanics force fields: potential form, combination rules, and vdw parameters,” Journal of the American Chemical Society 114, 7827–7843 (1992).
  70. P. M. Morse, “Diatomic molecules according to the wave mechanics. ii. vibrational levels,” Phys. Rev. 34, 57–64 (1929).
  71. K. Vanommeslaeghe, E. Hatcher, C. Acharya, S. Kundu, S. Zhong, J. Shim, E. Darian, O. Guvench, P. Lopes, I. Vorobyov,  and A. D. Mackerell Jr., “Charmm general force field: A force field for drug-like molecules compatible with the charmm all-atom additive biological force fields,” Journal of Computational Chemistry 31, 671–690 (2010).
  72. S. L. Mayo, B. D. Olafson,  and W. A. Goddard, “Dreiding: a generic force field for molecular simulations,” Journal of Physical Chemistry 94, 8897–8909 (1990).
  73. M. J. Robertson, J. Tirado-Rives,  and W. L. Jorgensen, “Improved peptide and protein torsional energetics with the opls-aa force field,” Journal of Chemical Theory and Computation 11, 3499–3509 (2015).
  74. J. E. Jones, “On the determination of molecular fields. —ii. from the equation of state of a gas,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 106, 463–477 (1924).
  75. R. A. Buckingham, “The classical equation of state of gaseous helium, neon and argon,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 168, 264–283 (1938).
  76. J. J. K. Chung, M. L. Brown,  and P. L. A. Popelier, “Transferability of buckingham parameters for short-range repulsion between topological atoms,” Journal of Chemical Theory and Computation 128, 4561–4572 (2024).
  77. J. R. Hart and A. K. Rappé, “van der waals functional forms for molecular simulations,” The Journal of chemical physics 97, 1109–1115 (1992).
  78. L. Yang, L. Sun,  and W.-Q. Deng, “Combination rules for morse-based van der waals force fields,” The Journal of Physical Chemistry A 122, 1672–1677 (2018).
  79. X. Wu and B. R. Brooks, “A double exponential potential for van der waals interaction,” AIP Advances 9, 065304 (2019).
  80. V. H. Man, X. Wu, X. HeXiang-Qun, X. R. Brooks,  and J. Wang, “Determination of van der waals parameters using a double exponential potential for nonbonded divalent metal cations in tip3p solvent,” Journal of chemical theory and computation 17, 1086–1097 (2021).
  81. J. T. Horton, S. Boothroyd, P. K. Behara, D. L. Mobley,  and D. J. Cole, “A transferable double exponential potential for condensed phase simulations of small molecules,” Digital Discovery 2, 1178–1187 (2023).
  82. M. Abraham, A. Alekseenko, V. Basov, C. Bergh, E. Briand, A. Brown, M. Doijade, G. Fiorin, S. Fleischmann, S. Gorelov, G. Gouaillardet, A. Grey, E. I. M., F. Jalalypour, J. Jordan, C. Kutzner, J. A. Lemkul, M. Lundborg, P. Merz, V. Miletic, D. Morozov, J. Nabet, S. Pall, A. Pasquadibisceglie, M. Pellegrino, H. Santuz, R. Schulz, T. Shugaeva, A. Shvetsov, A. Villa, S. Wingbermuehle, B. Hess,  and E. Lindahl, “Gromacs 2024.2 manual,”  (2024).
  83. S. Chmiela, V. Vassilev-Galindo, O. T. Unke, A. Kabylda, H. E. Sauceda, A. Tkatchenko,  and K.-R. Müller, “Accurate global machine learning force fields for molecules with hundreds of atoms,”  (2022), arXiv:2209.14865 [physics.chem-ph] .
  84. D. P. Kovács, I. Batatia, E. S. Arany,  and G. Csányi, “Evaluation of the MACE force field architecture: From medicinal chemistry to materials science,” The Journal of Chemical Physics 159, 044118 (2023b).
  85. O. T. Unke and M. Meuwly, “Physnet: A neural network for predicting energies, forces, dipole moments, and partial charges,” Journal of Chemical Theory and Computation 15, 3678–3693 (2019).
  86. M. S. Chen, J. Lee, H.-Z. Ye, T. C. Berkelbach, D. R. Reichman,  and T. E. Markland, “Data-efficient machine learning potentials from transfer learning of periodic correlated electronic structure methods: Liquid water at afqmc, ccsd, and ccsd(t) accuracy,” Journal of Chemical Theory and Computation 19, 4510–4519 (2023).
  87. M. Rossi, W. Fang,  and A. Michaelides, “Stability of complex biomolecular structures: van der waals, hydrogen bond cooperativity, and nuclear quantum effects,” The Journal of Physical Chemistry Letters 6, 4233–4238 (2015).
  88. K. Yao, J. E. Herr, D. Toth, R. Mckintyre,  and J. Parkhill, “The tensormol-0.1 model chemistry: a neural network augmented with long-range physics,” Chem. Sci. 9, 2261–2269 (2018).
  89. T. Plé, L. Lagardère,  and J.-P. Piquemal, “Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects,” Chem. Sci. 14, 12554–12569 (2023).
  90. O. I. Dylan Anstine, Roman Zubatyuk, “Aimnet2: A neural network potential to meet your neutral, charged, organic, and elemental-organic needs,”  (2024).
  91. B. Kozinsky, A. Musaelian, A. Johansson,  and S. Batzner, “Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (2023) pp. 1–12.
  92. O. T. Unke, M. Stöhr, S. Ganscha, T. Unterthiner, H. Maennel, S. Kashubin, D. Ahlin, M. Gastegger, L. M. Sandonas, J. T. Berryman, A. Tkatchenko,  and K.-R. Müller, “Biomolecular dynamics with machine-learned quantum-mechanical force fields trained on diverse chemical fragments,” Science Advances 10, eadn4397 (2024).
  93. Z. Cheng, J. Du, L. Zhang, J. Ma, W. Li,  and S. Li, “Building quantum mechanics quality force fields of proteins with the generalized energy-based fragmentation approach and machine learning,” Phys. Chem. Chem. Phys. 24, 1326–1337 (2022).
  94. S. L. J. Lahey and C. N. Rowley, “Simulating protein-ligand binding with neural network potentials,” Chem. Sci. 11, 2362–2368 (2020).
  95. D. A. Rufa, H. E. Bruce Macdonald, J. Fass, M. Wieder, P. B. Grinaway, A. E. Roitberg, O. Isayev,  and J. D. Chodera, “Towards chemical accuracy for alchemical free energy calculations with hybrid physics-based machine learning/molecular mechanics potentials,” BioRxiv , 2020–07 (2020).
  96. R. Galvelis, A. Varela-Rial, S. Doerr, R. Fino, P. Eastman, T. E. Markland, J. D. Chodera,  and G. De Fabritiis, “Nnp/mm: accelerating molecular dynamics simulations with machine learning potentials and molecular mechanics,” Journal of chemical information and modeling 63, 5701–5708 (2023).
  97. F. Sabanés Zariquiey, R. Galvelis, E. Gallicchio, J. D. Chodera, T. E. Markland,  and G. De Fabritiis, “Enhancing protein–ligand binding affinity predictions using neural network potentials,” Journal of Chemical Information and Modeling 64, 1481–1485 (2024).
  98. T. Jaffrelot Inizan, T. Plé, O. Adjoua, P. Ren, H. Gökcan, O. Isayev, L. Lagardère,  and J.-P. Piquemal, “Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects,” Chem. Sci. 14, 5438–5452 (2023).
  99. K. Zinovjev, L. Hedges, R. Montagud Andreu, C. Woods, I. Tuñón,  and M. W. van der Kamp, “emle-engine: A flexible electrostatic machine learning embedding package for multiscale molecular dynamics simulations,” Journal of Chemical Theory and Computation 20, 4514–4522 (2024), pMID: 38804055.
  100. D. W. Zhang and J. Z. H. Zhang, “Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein–molecule interaction energy,” The Journal of Chemical Physics 119, 3599–3605 (2003).
  101. X. He and J. Z. H. Zhang, “The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy,” The Journal of Chemical Physics 124, 184703 (2006).
  102. X. Wang, J. Liu, J. Z. H. Zhang,  and X. He, “Electrostatically embedded generalized molecular fractionation with conjugate caps method for full quantum mechanical calculation of protein energy,” The Journal of Physical Chemistry A 117, 7149–7161 (2013).
  103. W. Li, S. Li,  and Y. Jiang, “Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules,” The Journal of Physical Chemistry A 111, 2193–2199 (2007).
  104. H. Wang and W. Yang, “Toward building protein force fields by residue-based systematic molecular fragmentation and neural network,” Journal of Chemical Theory and Computation 15, 1409–1417 (2019).
  105. Z. Wang, Y. Han, J. Li,  and X. He, “Combining the fragmentation approach and neural network potential energy surfaces of fragments for accurate calculation of protein energy,” The Journal of Physical Chemistry B 124, 3027–3035 (2020b).
  106. Y. Han, Z. Wang, A. Chen, I. Ali, J. Cai, S. Ye,  and J. Li, “An inductive transfer learning force field (ITLFF) protocol builds protein force fields in seconds,” Briefings in Bioinformatics 23, bbab590 (2022).
  107. P. Thölke and G. D. Fabritiis, “Torchmd-net: Equivariant transformers for neural network based molecular potentials,”  (2022), arXiv:2202.02541 [cs.LG] .
  108. K. T. Schütt, O. T. Unke,  and M. Gastegger, “Equivariant message passing for the prediction of tensorial properties and molecular spectra,”  (2021), arXiv:2102.03150 [cs.LG] .
  109. D. K. Duvenaud, D. Maclaurin, J. Iparraguirre, R. Bombarell, T. Hirzel, A. Aspuru-Guzik,  and R. P. Adams, “Convolutional networks on graphs for learning molecular fingerprints,” in Advances in neural information processing systems (2015) pp. 2224–2232.
  110. T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” CoRR abs/1609.02907 (2016), arXiv:1609.02907 .
  111. J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals,  and G. E. Dahl, “Neural message passing for quantum chemistry,” in International conference on machine learning (PMLR, 2017) pp. 1263–1272.
  112. K. Xu, W. Hu, J. Leskovec,  and S. Jegelka, “How powerful are graph neural networks?” arXiv preprint arXiv:1810.00826  (2018).
  113. P. W. Battaglia, J. B. Hamrick, V. Bapst, A. Sanchez-Gonzalez, V. Zambaldi, M. Malinowski, A. Tacchetti, D. Raposo, A. Santoro, R. Faulkner, et al., “Relational inductive biases, deep learning, and graph networks,” arXiv preprint arXiv:1806.01261  (2018).
  114. J. Du, S. Zhang, G. Wu, J. M. F. Moura,  and S. Kar, “Topology Adaptive Graph Convolutional Networks,” arXiv:1710.10370 [cs, stat]  (2018), arXiv:1710.10370 [cs, stat] .
  115. F. Wu, T. Zhang, A. H. d. Souza Jr, C. Fifty, T. Yu,  and K. Q. Weinberger, “Simplifying graph convolutional networks,” arXiv preprint arXiv:1902.07153  (2019a).
  116. M. Wang, D. Zheng, Z. Ye, Q. Gan, M. Li, X. Song, J. Zhou, C. Ma, L. Yu, Y. Gai, et al., “Deep graph library: A graph-centric, highly-performant package for graph neural networks,” arXiv preprint arXiv:1909.01315  (2019a).
  117. Y. Wang, Y. Sun, Z. Liu, S. E. Sarma, M. M. Bronstein,  and J. M. Solomon, “Dynamic graph cnn for learning on point clouds,” Acm Transactions On Graphics (tog) 38, 1–12 (2019b).
  118. C. K. Joshi, C. Bodnar, S. V. Mathis, T. Cohen,  and P. Lió, “On the expressive power of geometric graph neural networks,” arXiv preprint arXiv:2301.09308  (2023).
  119. Y. Wang and T. Karaletsos, “Stochastic aggregation in graph neural networks,”  (2021), arXiv:2102.12648 [stat.ML] .
  120. P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò,  and Y. Bengio, “Graph attention networks,”  (2018), arXiv:1710.10903 [stat.ML] .
  121. F. Wu, T. Zhang, A. H. S. Jr., C. Fifty, T. Yu,  and K. Q. Weinberger, “Simplifying graph convolutional networks,” CoRR abs/1902.07153 (2019b), 1902.07153 .
  122. B. P. Chamberlain, J. Rowbottom, M. I. Gorinova, S. Webb, E. Rossi,  and M. M. Bronstein, “GRAND: graph neural diffusion,” CoRR abs/2106.10934 (2021), 2106.10934 .
  123. C. Cai and Y. Wang, “A note on over-smoothing for graph neural networks,”  (2020), arXiv:2006.13318 [cs.LG] .
  124. T. K. Rusch, M. M. Bronstein,  and S. Mishra, “A survey on oversmoothing in graph neural networks,”  (2023), arXiv:2303.10993 [cs.LG] .
  125. U. Alon and E. Yahav, “On the bottleneck of graph neural networks and its practical implications,” CoRR abs/2006.05205 (2020), 2006.05205 .
  126. J. Topping, F. D. Giovanni, B. P. Chamberlain, X. Dong,  and M. M. Bronstein, “Understanding over-squashing and bottlenecks on graphs via curvature,”  (2022), arXiv:2111.14522 [stat.ML] .
  127. G. Corso, L. Cavalleri, D. Beaini, P. Liò,  and P. Veličković, “Principal neighbourhood aggregation for graph nets,”  (2020), arXiv:2004.05718 [cs.LG] .
  128. V. K. Garg, S. Jegelka,  and T. S. Jaakkola, “Generalization and representational limits of graph neural networks,” CoRR abs/2002.06157 (2020), 2002.06157 .
  129. Y. Wang and K. Cho, “Non-convolutional graph neural networks,”  (2024), arXiv:2408.00165 [cs.LG] .
  130. K. T. Schütt, P.-J. Kindermans, H. E. Sauceda, S. Chmiela, A. Tkatchenko,  and K.-R. Müller, “Schnet: A continuous-filter convolutional neural network for modeling quantum interactions,”  (2017), arXiv:1706.08566 [stat.ML] .
  131. J. S. Smith, O. Isayev,  and A. E. Roitberg, “Ani-1: an extensible neural network potential with dft accuracy at force field computational cost,” Chemical Science 8, 3192–3203 (2017b).
  132. S. Villar, D. W. Hogg, K. Storey-Fisher, W. Yao,  and B. Blum-Smith, “Scalars are universal: Equivariant machine learning, structured like classical physics,”  (2023), arXiv:2106.06610 [cs.LG] .
  133. N. Thomas, T. E. Smidt, S. Kearnes, L. Yang, L. Li, K. Kohlhoff,  and P. Riley, “Tensor field networks: Rotation- and translation-equivariant neural networks for 3d point clouds,” CoRR abs/1802.08219 (2018), 1802.08219 .
  134. J. P. Perdew, K. Burke,  and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical review letters 77, 3865 (1996).
  135. A. Tkatchenko, R. A. DiStasio Jr, R. Car,  and M. Scheffler, “Accurate and efficient method for many-body van der waals interactions,” Physical review letters 108, 236402 (2012).
  136. R. Ramakrishnan, P. O. Dral, M. Rupp,  and O. A. Von Lilienfeld, “Quantum chemistry structures and properties of 134 kilo molecules,” Scientific data 1, 1–7 (2014).
  137. J. S. Smith, O. Isayev,  and A. E. Roitberg, “Ani-1, a data set of 20 million calculated off-equilibrium conformations for organic molecules,” Scientific data 4, 1–8 (2017c).
  138. A. S. Christensen, S. K. Sirumalla, Z. Qiao, M. B. O’Connor, D. G. A. Smith, F. Ding, P. J. Bygrave, A. Anandkumar, M. Welborn, F. R. Manby,  and T. F. M. III, “OrbNet Denali Training Data,”   (2021a), 10.6084/m9.figshare.14883867.v2.
  139. A. S. Christensen, S. K. Sirumalla, Z. Qiao, M. B. O’Connor, D. G. A. Smith, F. Ding, P. J. Bygrave, A. Anandkumar, M. Welborn, F. R. Manby,  and T. F. Miller, “Orbnet denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and dft accuracy,” The Journal of Chemical Physics 155 (2021b), 10.1063/5.0061990.
  140. A. Ullah and P. O. Dral, “Molecular quantum chemical data sets and databases for machine learning potentials,” arXiv preprint arXiv:2408.12058  (2024).
  141. C. N. Cavasotto, “Binding free energy calculation using quantum mechanics aimed for drug lead optimization,” Quantum mechanics in drug discovery , 257–268 (2020).
  142. A. E. A. Allen, N. Lubbers, S. Matin, J. Smith, R. Messerly, S. Tretiak,  and K. Barros, “Learning together: Towards foundational models for machine learning interatomic potentials with meta-learning,”  (2023), arXiv:2307.04012 [physics.chem-ph] .
  143. D. H. Wolpert, “The lack of a priori distinctions between learning algorithms,” Neural computation 8, 1341–1390 (1996).
  144. A. S. Christensen and O. A. von Lilienfeld, “On the role of gradients for machine learning of molecular energies and forces,”  (2020b), arXiv:2007.09593 [physics.chem-ph] .
  145. D. P. Kovács, C. v. d. Oord, J. Kucera, A. E. Allen, D. J. Cole, C. Ortner,  and G. Csányi, “Linear atomic cluster expansion force fields for organic molecules: beyond rmse,” Journal of chemical theory and computation 17, 7696–7711 (2021).
  146. I. Batatia, S. Batzner, D. P. Kovács, A. Musaelian, G. N. C. Simm, R. Drautz, C. Ortner, B. Kozinsky,  and G. Csányi, “The design space of e(3)-equivariant atom-centered interatomic potentials,”  (2022), arXiv:2205.06643 [stat.ML] .
  147. P. Eastman, P. K. Behara, D. Dotson, R. Galvelis, J. Herr, J. Horton, Y. Mao, J. Chodera, B. Pritchard, Y. Wang, G. De Fabritiis,  and T. Markland, “Spice 2.0.1,”  (2024a).
  148. D. G. Smith, D. Altarawy, L. A. Burns, M. Welborn, L. N. Naden, L. Ward, S. Ellis, B. P. Pritchard,  and T. D. Crawford, “The molssi qcarchive project: An open-source platform to compute, organize, and share quantum chemistry data,” Wiley Interdisciplinary Reviews: Computational Molecular Science 11, e1491 (2021).
  149. J. A. Vita, E. G. Fuemmeler, A. Gupta, G. P. Wolfe, A. Q. Tao, R. S. Elliott, S. Martiniani,  and E. B. Tadmor, “Colabfit exchange: open-access datasets for data-driven interatomic potentials,”  (2023), arXiv:2306.11071 [cond-mat.mtrl-sci] .
  150. Y. Yang, S. Zhang, K. D. Ranasinghe, O. Isayev,  and A. E. Roitberg, “Machine learning of reactive potentials,” Annual Review of Physical Chemistry 75, 371–395 (2024).
  151. U. Rivero, O. T. Unke, M. Meuwly,  and S. Willitsch, “Reactive atomistic simulations of Diels-Alder reactions: The importance of molecular rotations,” The Journal of Chemical Physics 151, 104301 (2019).
  152. S. Zhang, M. Z. Makoś, R. B. Jadrich, E. Kraka, K. Barros, B. T. Nebgen, S. Tretiak, O. Isayev, N. Lubbers, R. A. Messerly, et al., “Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential,” Nature Chemistry 16, 727–734 (2024).
  153. M. Gastegger and P. Marquetand, “High-dimensional neural network potentials for organic reactions and an improved training algorithm,” Journal of Chemical Theory and Computation 11, 2187–2198 (2015).
  154. M. Schreiner, A. Bhowmik, T. Vegge, J. Busk,  and O. Winther, “Transition1x - a dataset for building generalizable reactive machine learning potentials,” Scientific Data 9, 779 (2022).
  155. T. A. Young, T. Johnston-Wood, H. Zhang,  and F. Duarte, “Reaction dynamics of diels–alder reactions from machine learned potentials,” Phys. Chem. Chem. Phys. 24, 20820–20827 (2022).
  156. X. Pan, J. Yang, R. Van, E. Epifanovsky, J. Ho, J. Huang, J. Pu, Y. Mei, K. Nam,  and Y. Shao, “Machine-learning-assisted free energy simulation of solution-phase and enzyme reactions,” Journal of Chemical Theory and Computation 17, 5745–5758 (2021).
  157. T. Devergne, T. Magrino, F. Pietrucci,  and A. M. Saitta, “Combining machine learning approaches and accurate ab initio enhanced sampling methods for prebiotic chemical reactions in solution,” Journal of Chemical Theory and Computation 18, 5410–5421 (2022).
  158. M. Yang, L. Bonati, D. Polino,  and M. Parrinello, “Using metadynamics to build neural network potentials for reactive events: the case of urea decomposition in water,” Catalysis Today 387, 143–149 (2022), 100 years of CASALE SA: a scientific perspective on catalytic processes.
  159. Z. Benayad, R. David,  and G. Stirnemann, “Prebiotic chemical reactivity in solution with quantum accuracy and microsecond sampling using neural network potentials,” Proceedings of the National Academy of Sciences 121, e2322040121 (2024).
  160. I.-B. Magdău, D. J. Arismendi-Arrieta, H. E. Smith, C. P. Grey, K. Hermansson,  and G. Csányi, “Machine learning force fields for molecular liquids: Ethylene carbonate/ethyl methyl carbonate binary solvent,” npj Computational Materials 9, 146 (2023).
  161. S. Boothroyd, L.-P. Wang, D. L. Mobley, J. D. Chodera,  and M. R. Shirts, “Open force field evaluator: An automated, efficient, and scalable framework for the estimation of physical properties from molecular simulation,” Journal of chemical theory and computation 18, 3566–3576 (2022).
  162. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke,  and T. E. Oliphant, “Array programming with numpy,” Nature 585, 357–362 (2020).
  163. J. R. Maple, M.-J. Hwang, T. P. Stockfisch, U. Dinur, M. Waldman, C. S. Ewig,  and A. T. Hagler, “Derivation of class II force fields. I. methodology and quantum force field for the alkyl functional group and alkane molecules,” Journal of Computational Chemistry 15, 162–182 (1994a).
  164. M. J. Hwang, T. Stockfisch,  and A. Hagler, “Derivation of class ii force fields. 2. derivation and characterization of a class ii force field, cff93, for the alkyl functional group and alkane molecules,” Journal of the American Chemical Society 116, 2515–2525 (1994).
  165. J. Maple, M.-J. Hwang, T. Stockfisch,  and A. Hagler, “Derivation of class ii force fields. iii. characterization of a quantum force field for alkanes,” Israel Journal of Chemistry 34, 195–231 (1994b).
  166. S. R. Xie, M. Rupp,  and R. G. Hennig, “Ultra-fast interpretable machine-learning potentials,” npj Computational Materials 9 (2023), 10.1038/s41524-023-01092-7.
  167. J. A. Lemkul, J. Huang, B. Roux,  and A. D. J. MacKerell, “An empirical polarizable force field based on the classical drude oscillator model: Development history and recent applicationss,” Chemical Reviews 116, 4983–5013 (2016).
  168. Y. Shi, Z. Xia, J. Zhang, R. Best, C. Wu, J. W. Ponder,  and P. Ren, “Polarizable atomic multipole-based amoeba force field for proteins,” Journal of chemical theory and computation 9, 4046–4063 (2013).
  169. A. Illarionov, S. Sakipov, L. Pereyaslavets, I. V. Kurnikov, G. Kamath, O. Butin, E. Voronina, I. Ivahnenko, I. Leontyev, G. Nawrocki, M. Darkhovskiy, M. Olevanov, Y. K. Cherniavskyi, C. Lock, S. Greenslade, S. K. Sankaranarayanan, M. G. Kurnikova, J. Potoff, R. D. Kornberg, M. Levitt,  and B. Fain, “Combining force fields and neural networks for an accurate representation of chemically diverse molecular interactions,” Journal of the American Chemical Society 145, 23620–23629 (2023).
  170. A. C. T. v. Duin, S. Dasgupta, F. Lorant,  and W. A. Goddard, “Reaxff: A reactive force field for hydrocarbons,” The Journal of Physical Chemistry A 105, 9396–9409 (2001).
  171. M. C. Kaymak, A. Rahnamoun, K. A. O’Hearn, A. C. T. v. Duin, K. M. J. Merz,  and H. M. Aktulga, “Jax-reaxff: A gradient-based framework for fast optimization of reactive force fields,” Journal of chemical theory and computation 18, 5181–5194 (2022).
  172. A. Warshel and R. M. Weiss, “An empirical valence bond approach for comparing reactions in solutions and in enzymes,” Journal of the American Chemical Society 102, 6218–6226 (1980).
  173. J. Lobaugh and G. A. Voth, “The quantum dynamics of an excess proton in water,” The Journal of Chemical Physics 104, 2056–2069 (1996).
  174. D. E. Sagnella and M. E. Tuckerman, “An empirical valence bond model for proton transfer in water,” The Journal of Chemical Physics 108, 2073–2083 (1998).
  175. U. W. Schmitt and G. A. Voth, “Multistate empirical valence bond model for proton transport in water,” The Journal of Physical Chemistry B 102, 5547–5551 (1998).
  176. J. Åqvist and A. Warshel, “Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches,” Chemical Reviews 93, 2523–2544 (1993).
  177. A. E. A. Allen and G. Csányi, “Toward transferable empirical valence bonds: Making classical force fields reactive,” The Journal of Chemical Physics 160, 124108 (2024).
  178. L.-P. Wang, J. Chen,  and T. Van Voorhis, “Systematic parametrization of polarizable force fields from quantum chemistry data,” Journal of chemical theory and computation 9, 452–460 (2013).
  179. L.-P. Wang, T. J. Martinez,  and V. S. Pande, “Building force fields: An automatic, systematic, and reproducible approach,” The journal of physical chemistry letters 5, 1885–1891 (2014).
  180. S. Thaler and J. Zavadlav, “Learning neural network potentials from experimental data via differentiable trajectory reweighting,” Nature communications 12, 6884 (2021).
  181. B. J. Befort, R. S. DeFever, G. M. Tow, A. W. Dowling,  and E. J. Maginn, “Machine learning directed optimization of classical molecular modeling force fields,” Journal of Chemical Information and Modeling 61, 4400–4414 (2021).
  182. X. Wang, J. Li, L. Yang, F. Chen, Y. Wang, J. Chang, J. Chen, W. Feng, L. Zhang,  and K. Yu, “Dmff: An open-source automatic differentiable platform for molecular force field development and molecular dynamics simulation,” Journal of Chemical Theory and Computation 19, 5897–5909 (2023).
  183. K. B. Koziara, M. Stroet, A. K. Malde,  and A. E. Mark, “Testing and validation of the automated topology builder (atb) version 2.0: prediction of hydration free enthalpies,” Journal of Computer-Aided Molecular Design 28, 221–233 (2014).
  184. R. M. Betz and R. C. Walker, “Paramfit: Automated optimization of force field parameters for molecular dynamics simulations,” Journal of computational chemistry 36, 79–87 (2015).
  185. E. Harder, W. Damm, J. Maple, C. Wu, M. Reboul, J. Y. Xiang, L. Wang, D. Lupyan, M. K. Dahlgren, J. L. Knight, et al., “Opls3: a force field providing broad coverage of drug-like small molecules and proteins,” Journal of chemical theory and computation 12, 281–296 (2016).
  186. J. T. Horton, S. Boothroyd, J. Wagner, J. A. Mitchell, T. Gokey, D. L. Dotson, P. K. Behara, V. K. Ramaswamy, M. Mackey, J. D. Chodera, J. Anwar, D. L. Mobley,  and D. J. Cole, “Open force field bespokefit: Automating bespoke torsion parametrization at scale,” Journal of Chemical Information and Modeling 62, 5622–5633 (2022).
  187. A. Kumar and A. D. J. MacKerell, “Ffparam-v2.0: A comprehensive tool for charmm additive and drude polarizable force-field parameter optimization and validation,” The Journal of Physical Chemistry B 128, 4385–4395 (2024).
  188. J. A. Maier, C. Martinez, K. Kasavajhala, L. Wickstrom, K. E. Hauser,  and C. Simmerling, “ff14sb: improving the accuracy of protein side chain and backbone parameters from ff99sb,” Journal of chemical theory and computation 11, 3696–3713 (2015).
  189. M. Zgarbová, J. Sponer, M. Otyepka, T. E. Cheatham III, R. Galindo-Murillo,  and P. Jurecka, “Refinement of the sugar–phosphate backbone torsion beta for amber force fields improves the description of z-and b-dna,” Journal of chemical theory and computation 11, 5723–5736 (2015).
  190. R. Galindo-Murillo, J. C. Robertson, M. Zgarbová, J. Šponer, M. Otyepka, P. Jurečka,  and T. E. Cheatham III, “Assessing the current state of amber force field modifications for dna,” Journal of chemical theory and computation 12, 4114–4127 (2016).
  191. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey,  and M. L. Klein, “Comparison of simple potential functions for simulating liquid water,” The Journal of chemical physics 79, 926–935 (1983).
  192. H. W. Horn, W. C. Swope, J. W. Pitera, J. D. Madura, T. J. Dick, G. L. Hura,  and T. Head-Gordon, “Development of an improved four-site water model for biomolecular simulations: Tip4p-ew,” The Journal of chemical physics 120, 9665–9678 (2004).
  193. S. Izadi, R. Anandakrishnan,  and A. V. Onufriev, “Building water models: A different approach,” The Journal of Physical Chemistry Letters 5, 3863–3871 (2014).
  194. I. S. Joung and T. E. Cheatham III, “Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations,” The journal of physical chemistry B 112, 9020–9041 (2008).
  195. I. S. Joung and T. E. Cheatham III, “Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters,” The Journal of Physical Chemistry B 113, 13279–13290 (2009).
  196. P. Li, B. P. Roberts, D. K. Chakravorty,  and K. M. Merz Jr, “Rational design of particle mesh ewald compatible lennard-jones parameters for+ 2 metal cations in explicit solvent,” Journal of chemical theory and computation 9, 2733–2748 (2013).
  197. P. Li and K. M. Merz Jr, “Taking into account the ion-induced dipole interaction in the nonbonded model of ions,” Journal of chemical theory and computation 10, 289–297 (2014).
  198. P. Li, L. F. Song,  and K. M. Merz Jr, “Parameterization of highly charged metal ions using the 12-6-4 lj-type nonbonded model in explicit water,” The Journal of Physical Chemistry B 119, 883–895 (2015).
  199. C. J. Dickson, R. C. Walker,  and I. R. Gould, “Lipid21: complex lipid membrane simulations with amber,” Journal of chemical theory and computation 18, 1726–1736 (2022).
  200. K. N. Kirschner, A. B. Yongye, S. M. Tschampel, J. González-Outeiriño, C. R. Daniels, B. L. Foley,  and R. J. Woods, “Glycam06: a generalizable biomolecular force field. carbohydrates,” Journal of computational chemistry 29, 622–655 (2008).
  201. M. L. DeMarco and R. J. Woods, “Atomic-resolution conformational analysis of the gm3 ganglioside in a lipid bilayer and its implications for ganglioside–protein recognition at membrane surfaces,” Glycobiology 19, 344–355 (2009).
  202. M. L. DeMarco, R. J. Woods, J. H. Prestegard,  and F. Tian, “Presentation of membrane-anchored glycosphingolipids determined from molecular dynamics simulations and nmr paramagnetic relaxation rate enhancement,” Journal of the American Chemical Society 132, 1334–1338 (2010).
  203. J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman,  and D. A. Case, “Development and testing of a general amber force field,” Journal of computational chemistry 25, 1157–1174 (2004).
  204. J. Wang, W. Wang, P. A. Kollman,  and D. A. Case, “Automatic atom type and bond type perception in molecular mechanical calculations,” Journal of molecular graphics and modelling 25, 247–260 (2006).
  205. G. A. Khoury, J. P. Thompson, J. Smadbeck, C. A. Kieslich,  and C. A. Floudas, “Forcefield_ptm: Ab initio charge and amber forcefield parameters for frequently occurring post-translational modifications,” Journal of chemical theory and computation 9, 5653–5674 (2013).
  206. R. Aduri, B. T. Psciuk, P. Saro, H. Taniga, H. B. Schlegel,  and J. SantaLucia, “Amber force field parameters for the naturally occurring modified nucleosides in rna,” Journal of chemical theory and computation 3, 1464–1475 (2007).
  207. D. L. Mobley, C. C. Bannan, A. Rizzi, C. I. Bayly, J. D. Chodera, V. T. Lim, N. M. Lim, K. A. Beauchamp, D. R. Slochower, M. R. Shirts, et al., “Escaping atom types in force fields using direct chemical perception,” Journal of chemical theory and computation 14, 6076–6092 (2018).
  208. M. Stroet, B. Caron, M. S. Engler, J. v. d. Woning, A. Kauffmann, M. v. Dijk, M. El-Kebir, K. M. Visscher, J. Holownia, C. Macfarlane, B. J. Bennion, S. Gelpi-Dominguez, F. C. Lightstone, T. v. d. Storm, D. P. Geerke, A. E. Mark,  and G. W. Klau, “Oframp: a fragment-based tool to facilitate the parametrization of large molecules,” Journal of computer-aided molecular design 37, 357–371 (2023).
  209. J. D. Yesselman, D. J. Price, J. L. Knight,  and C. L. Brooks III, “Match: An atom-typing toolset for molecular mechanics force fields,” Journal of computational chemistry 33, 189–202 (2012).
  210. L. Wang, P. K. Behara, M. W. Thompson, T. Gokey, Y. Wang, J. R. Wagner, D. J. Cole, M. K. Gilson, M. R. Shirts,  and D. L. Mobley, “The open force field initiative: Open software and open science for molecular modeling,” The Journal of Physical Chemistry B  (2024a).
  211. J. Wagner, M. Thompson, D. L. Mobley, J. Chodera, C. Bannan, A. Rizzi, trevorgokey, D. L. Dotson, J. A. Mitchell, jaimergp, Camila, P. Behara, C. Bayly, JoshHorton, I. Pulido, L. Wang, V. Lim, S. Sasmal, SimonBoothroyd, A. Dalke, D. Smith, B. Westbrook, J. Horton, L.-P. Wang, R. Gowers, Z. Zhao, C. Davel,  and Y. Zhao, “openforcefield/openff-toolkit: 0.15.2 Minor feature release,”  (2024).
  212. A. R. McIsaac, P. K. Behara, T. Gokey, C. Cavender, J. Horton, L. Wang, B. R. Westbrook, M. W. Thompson, M. Osato, H. M. Baumann, H. Jang, J. Wagne, D. Cole, C. Bayly,  and D. Mobley, “openforcefield/openff-forcefields,”  (2024).
  213. K. Roos, C. Wu, W. Damm, M. Reboul, J. M. Stevenson, C. Lu, M. K. Dahlgren, S. Mondal, W. Chen, L. Wang, R. Abel, R. A. Friesner,  and E. D. Harder, “Opls3e: Extending force field coverage for drug-like small molecules,” Journal of Chemical Theory and Computation 15, 1863–1874 (2019).
  214. T. Gokey and D. L. Mobley, “Hierarchical clustering of chemical space using binary-encoded smarts for building data-driven chemical perception models,”   (2023).
  215. Y. Wang, J. Fass, B. Kaminow, J. E. Herr, D. Rufa, I. Zhang, I. Pulido, M. Henry, H. E. Bruce Macdonald, K. Takaba,  and J. D. Chodera, “End-to-end differentiable construction of molecular mechanics force fields,” Chem. Sci. 13, 12016–12033 (2022).
  216. K. Takaba, I. Pulido, P. K. Behara, C. E. Cavender, A. J. Friedman, M. M. Henry, H. M. Opeskin, C. R. Iacovella, A. M. Nagle, A. M. Payne, M. R. Shirts, D. L. Mobley, J. D. Chodera,  and Y. Wang, “Machine-learned molecular mechanics force field for the simulation of protein-ligand systems and beyond,”  (2023), arXiv:2307.07085 [physics.chem-ph] .
  217. G. Chen, T. Jaffrelot Inizan, T. Plé, L. Lagardère, J.-P. Piquemal,  and Y. Maday, “Advancing force fields parameterization: A directed graph attention networks approach,” Journal of Chemical Theory and Computation 20, 5558–5569 (2024).
  218. L. Seute, E. Hartmann, J. Stühmer,  and G. Frauke, “Grappa – a machine learned molecular mechanics force field,” arXiv preprint arXiv:2404.00050  (2024).
  219. M. Thurlemann, L. Boselt,  and S. Riniker, “Regularized by physics: Graph neural network parametrized potentials for the description of intermolecular interactions,” Journal of Chemical Theory and Computation 19, 562–579 (2023).
  220. M. T. Lehner, P. Katzberger, N. Maeder, C. C. Schiebroek, J. Teetz, G. A. Landrum,  and S. Riniker, “Dash: Dynamic attention-based substructure hierarchy for partial charge assignment,” Journal of Chemical Information and Modeling 63, 6014–6028 (2023).
  221. Y. Wang, I. Pulido, K. Takaba, B. Kaminow, J. Scheen, L. Wang,  and J. D. Chodera, “Espalomacharge: Machine learning-enabled ultrafast partial charge assignment,” The Journal of Physical Chemistry A 128, 4160–4167 (2024b).
  222. Y. Wang, J. Fass, C. D. Stern, K. Luo,  and J. Chodera, “Graph nets for partial charge prediction,”  (2019c), arXiv:1909.07903 [physics.comp-ph] .
  223. Y. Wang, Graph Machine Learning for (Bio) Molecular Modeling and Force Field Construction (Weill Medical College of Cornell University, 2023).
  224. S. Passaro and C. L. Zitnick, “Reducing so(3) convolutions to so(2) for efficient equivariant gnns,”  (2023), arXiv:2302.03655 [cs.LG] .
  225. S. Luo, T. Chen,  and A. S. Krishnapriyan, “Enabling efficient equivariant operations in the fourier basis via gaunt tensor products,”  (2024), arXiv:2401.10216 [cs.LG] .
  226. B. Cheng, “Cartesian atomic cluster expansion for machine learning interatomic potentials,”  (2024), arXiv:2402.07472 [physics.comp-ph] .
  227. B. Smit, P. Hilbers, K. Esselink, L. Rupert, N. Van Os,  and A. Schlijper, “Computer simulations of a water/oil interface in the presence of micelles,” Nature 348, 624–625 (1990).
  228. M. Müller, K. Katsov,  and M. Schick, “Biological and synthetic membranes: What can be learned from a coarse-grained description?” Physics Reports 434, 113–176 (2006).
  229. S. J. Marrink, H. J. Risselada, S. Yefimov, D. P. Tieleman,  and A. H. De Vries, “The martini force field: coarse grained model for biomolecular simulations,” The journal of physical chemistry B 111, 7812–7824 (2007).
  230. P. C. Souza, R. Alessandri, J. Barnoud, S. Thallmair, I. Faustino, F. Grünewald, I. Patmanidis, H. Abdizadeh, B. M. Bruininks, T. A. Wassenaar, et al., “Martini 3: a general purpose force field for coarse-grained molecular dynamics,” Nature methods 18, 382–388 (2021).
  231. J. Wang, S. Olsson, C. Wehmeyer, A. Pérez, N. E. Charron, G. De Fabritiis, F. Noé,  and C. Clementi, “Machine learning of coarse-grained molecular dynamics force fields,” ACS central science 5, 755–767 (2019d).
  232. W. Wang and R. Gómez-Bombarelli, “Coarse-graining auto-encoders for molecular dynamics,” npj Computational Materials 5, 125 (2019).
  233. S. Yang and R. Gómez-Bombarelli, “Chemically transferable generative backmapping of coarse-grained proteins,” arXiv preprint arXiv:2303.01569  (2023).
  234. S. Wang, B. Z. Li, M. Khabsa, H. Fang,  and H. Ma, “Linformer: Self-attention with linear complexity,”  (2020c), arXiv:2006.04768 [cs.LG] .
  235. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser,  and I. Polosukhin, “Attention is all you need,”  (2023a), arXiv:1706.03762 [cs.CL] .
  236. J. D. Gale, L. M. LeBlanc, P. R. Spackman, A. Silvestri,  and P. Raiteri, “A universal force field for materials, periodic gfn-ff: implementation and examination,” Journal of Chemical Theory and Computation 17, 7827–7849 (2021).
  237. M. R. Gunner, T. Murakami, A. S. Rustenburg, M. Işık,  and J. D. Chodera, “Standard state free energies, not pk as, are ideal for describing small molecule protonation and tautomeric states,” Journal of Computer-Aided Molecular Design 34, 561–573 (2020).
  238. P. Eastman, B. P. Pritchard, J. D. Chodera,  and T. E. Markland, “Nutmeg and spice: Models and data for biomolecular machine learning,”  (2024b), arXiv:2406.13112 [physics.chem-ph] .
  239. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser,  and I. Polosukhin, “Attention is all you need,”  (2023b), arXiv:1706.03762 [cs.CL] .
  240. S. M. Larson, C. D. Snow, M. Shirts,  and V. S. Pande, “Folding@home and genome@home: Using distributed computing to tackle previously intractable problems in computational biology,”  (2009), arXiv:0901.0866 [physics.bio-ph] .
  241. M. Thürlemann, L. Böselt,  and S. Riniker, “Learning atomic multipoles: Prediction of the electrostatic potential with equivariant graph neural networks,” Journal of Chemical Theory and Computation 18, 1701–1710 (2022), pMID: 35112866, https://doi.org/10.1021/acs.jctc.1c01021 .
  242. A. K. Rappe and W. A. Goddard III, “Charge equilibration for molecular dynamics simulations,” The Journal of Physical Chemistry 95, 3358–3363 (1991).
  243. T. W. Ko, J. A. Finkler, S. Goedecker,  and J. Behler, “A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer,” Nat. Commun. 12, 1–11 (2021).
  244. D. M. Anstine and O. Isayev, “Machine learning interatomic potentials and long-range physics,” The Journal of Physical Chemistry A 127, 2417–2431 (2023).
  245. J. Westermayr, S. Chaudhuri, A. Jeindl, O. T. Hofmann,  and R. J. Maurer, “Long-range dispersion-inclusive machine learning potentials for structure search and optimization of hybrid organic–inorganic interfaces,” Digital Discovery 1, 463–475 (2022).
  246. N. T. P. Tu, N. Rezajooei, E. R. Johnson,  and C. N. Rowley, “A neural network potential with rigorous treatment of long-range dispersion,” Digital Discovery  (2023).
  247. L. Böselt, M. Thürlemann,  and S. Riniker, “Machine learning in qm/mm molecular dynamics simulations of condensed-phase systems,” Journal of Chemical Theory and Computation 17, 2641–2658 (2021).
  248. H. M. Senn and W. Thiel, “QM/MM methods for biomolecular systems,” Angew. Chem. Int. Ed Engl. 48, 1198–1229 (2009).
  249. D. J. Cole, L. Mones,  and G. Csányi, “A machine learning based intramolecular potential for a flexible organic molecule,” Faraday Discussions 224, 247–264 (2020).
  250. J. Karwounopoulos, Z. Wu, S. Tkaczyk, S. Wang, A. Baskerville, K. Ranasinghe, T. Langer, G. P. Wood, M. Wieder,  and S. Boresch, “Insights and challenges in correcting force field based solvation free energies using a neural network potential,” The Journal of Physical Chemistry B 128, 6693–6703 (2024).
  251. B. Lier, P. Poliak, P. Marquetand, J. Westermayr,  and C. Oostenbrink, “BuRNN: Buffer region neural network approach for Polarizable-Embedding neural Network/Molecular mechanics simulations,” J. Phys. Chem. Lett. , 3812–3818 (2022).
  252. A. W. H. Grubmüller, H. Heller and K. Schulten, “Generalized verlet algorithm for efficient molecular dynamics simulations with long-range interactions,” Molecular Simulation 6, 121–142 (1991).
  253. M. Tuckerman, B. J. Berne,  and G. J. Martyna, “Reversible multiple time scale molecular dynamics,” The Journal of Chemical Physics 97, 1990–2001 (1992).
  254. D. T. W.B. Streett and G. Saville, “Multiple time-step methods in molecular dynamics,” Molecular Physics 35, 639–648 (1978).
  255. P. Minary, M. E. Tuckerman,  and G. J. Martyna, “Long time molecular dynamics for enhanced conformational sampling in biomolecular systems,” Phys. Rev. Lett. 93, 150201 (2004).
  256. P. F. Batcho, D. A. Case,  and T. Schlick, “Optimized particle-mesh Ewald/multiple-time step integration for molecular dynamics simulations,” The Journal of Chemical Physics 115, 4003–4018 (2001).
  257. M. Guidon, F. Schiffmann, J. Hutter,  and J. VandeVondele, “Ab initio molecular dynamics using hybrid density functionals,” The Journal of Chemical Physics 128, 214104 (2008).
  258. R. P. Steele, “Communication: Multiple-timestep ab initio molecular dynamics with electron correlation,” The Journal of Chemical Physics 139, 011102 (2013).
  259. N. Luehr, T. E. Markland,  and T. J. Martínez, “Multiple time step integrators in ab initio molecular dynamics,” The Journal of Chemical Physics 140, 084116 (2014).
  260. W. Wang, S. Axelrod,  and R. Gómez-Bombarelli, “Differentiable molecular simulations for control and learning,”  (2020), arXiv:2003.00868 [physics.comp-ph] .
  261. J. G. Greener and D. T. Jones, “Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins,” PloS one 16, e0256990 (2021).
  262. P. Kidger, R. T. Q. Chen,  and T. J. Lyons, “"hey, that’s not an ode": Faster ode adjoints via seminorms.” International Conference on Machine Learning  (2021).
  263. R. T. Q. Chen, Y. Rubanova, J. Bettencourt,  and D. Duvenaud, “Neural ordinary differential equations,” Advances in Neural Information Processing Systems  (2018).
  264. L. S. Pontryagin, Mathematical theory of optimal processes (Routledge, 2018).
  265. S. S. Schoenholz and E. D. Cubuk, “Jax m.d. a framework for differentiable physics,” in Advances in Neural Information Processing Systems, Vol. 33 (Curran Associates, Inc., 2020).
  266. S. Doerr, M. Majewski, A. Pérez, A. Kramer, C. Clementi, F. Noe, T. Giorgino,  and G. De Fabritiis, “Torchmd: A deep learning framework for molecular simulations,” Journal of chemical theory and computation 17, 2355–2363 (2021).
  267. J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne,  and Q. Zhang, “JAX: composable transformations of Python+NumPy programs,”  (2018).
  268. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai,  and S. Chintala, “Pytorch: An imperative style, high-performance deep learning library,”  (2019), arXiv:1912.01703 [cs.LG] .
  269. NVIDIA,  (2017).
  270. Y. Zhao, “timemachine,” https://github.com/proteneer/timemachine (2024).
  271. R. O. Dror, C. Young,  and D. E. Shaw, “Anton, a special-purpose molecular simulation machine.”  (2011).
  272. D. E. Shaw, P. J. Adams, A. Azaria, J. A. Bank, B. Batson, A. Bell, M. Bergdorf, J. Bhatt, J. A. Butts, T. Correia, et al., “Anton 3: twenty microseconds of molecular dynamics simulation before lunch,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (2021) pp. 1–11.
  273. R. Bommasani, D. A. Hudson, E. Adeli, R. Altman, S. Arora, S. von Arx, M. S. Bernstein, J. Bohg, A. Bosselut, E. Brunskill, E. Brynjolfsson, S. Buch, D. Card, R. Castellon, N. Chatterji, A. Chen, K. Creel, J. Q. Davis, D. Demszky, C. Donahue, M. Doumbouya, E. Durmus, S. Ermon, J. Etchemendy, K. Ethayarajh, L. Fei-Fei, C. Finn, T. Gale, L. Gillespie, K. Goel, N. Goodman, S. Grossman, N. Guha, T. Hashimoto, P. Henderson, J. Hewitt, D. E. Ho, J. Hong, K. Hsu, J. Huang, T. Icard, S. Jain, D. Jurafsky, P. Kalluri, S. Karamcheti, G. Keeling, F. Khani, O. Khattab, P. W. Koh, M. Krass, R. Krishna, R. Kuditipudi, A. Kumar, F. Ladhak, M. Lee, T. Lee, J. Leskovec, I. Levent, X. L. Li, X. Li, T. Ma, A. Malik, C. D. Manning, S. Mirchandani, E. Mitchell, Z. Munyikwa, S. Nair, A. Narayan, D. Narayanan, B. Newman, A. Nie, J. C. Niebles, H. Nilforoshan, J. Nyarko, G. Ogut, L. Orr, I. Papadimitriou, J. S. Park, C. Piech, E. Portelance, C. Potts, A. Raghunathan, R. Reich, H. Ren, F. Rong, Y. Roohani, C. Ruiz, J. Ryan, C. Ré, D. Sadigh, S. Sagawa, K. Santhanam, A. Shih, K. Srinivasan, A. Tamkin, R. Taori, A. W. Thomas, F. Tramèr, R. E. Wang, W. Wang, B. Wu, J. Wu, Y. Wu, S. M. Xie, M. Yasunaga, J. You, M. Zaharia, M. Zhang, T. Zhang, X. Zhang, Y. Zhang, L. Zheng, K. Zhou,  and P. Liang, “On the opportunities and risks of foundation models,”  (2022), arXiv:2108.07258 [cs.LG] .
  274. L. Chanussot, A. Das, S. Goyal, T. Lavril, M. Shuaibi, M. Riviere, K. Tran, J. Heras-Domingo, C. Ho, W. Hu, A. Palizhati, A. Sriram, B. Wood, J. Yoon, D. Parikh, C. L. Zitnick,  and Z. Ulissi, “Open catalyst 2020 (oc20) dataset and community challenges,” ACS Catalysis 11, 6059–6072 (2021).
  275. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, et al., “Commentary: The materials project: A materials genome approach to accelerating materials innovation,” APL materials 1 (2013).
  276. C. Zang and F. Wang, “Moflow: An invertible flow model for generating molecular graphs,” in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery; Data Mining, KDD ’20 (ACM, 2020).
  277. W. Jin, R. Barzilay,  and T. Jaakkola, “Junction tree variational autoencoder for molecular graph generation,”  (2019), arXiv:1802.04364 [cs.LG] .
  278. C. Shi, M. Xu, Z. Zhu, W. Zhang, M. Zhang,  and J. Tang, “Graphaf: a flow-based autoregressive model for molecular graph generation,”  (2020), arXiv:2001.09382 [cs.LG] .
  279. E. Mansimov, O. Mahmood, S. Kang,  and K. Cho, “Molecular geometry prediction using a deep generative graph neural network,” Scientific Reports 9 (2019), 10.1038/s41598-019-56773-5.
  280. E. Hoogeboom, V. G. Satorras, C. Vignac,  and M. Welling, “Equivariant diffusion for molecule generation in 3d,”  (2022), arXiv:2203.17003 [cs.LG] .
  281. J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, et al., “Highly accurate protein structure prediction with alphafold,” nature 596, 583–589 (2021).
  282. J. Abramson, J. Adler, J. Dunger, R. Evans, T. Green, A. Pritzel, O. Ronneberger, L. Willmore, A. J. Ballard, J. Bambrick, et al., “Accurate structure prediction of biomolecular interactions with alphafold 3,” Nature , 1–3 (2024).
  283. G. Ahdritz, N. Bouatta, C. Floristean, S. Kadyan, Q. Xia, W. Gerecke, T. J. O’Donnell, D. Berenberg, I. Fisk, N. Zanichelli, et al., “Openfold: Retraining alphafold2 yields new insights into its learning mechanisms and capacity for generalization,” Nature Methods , 1–11 (2024).
  284. L. Klein, A. Y. K. Foong, T. E. Fjelde, B. Mlodozeniec, M. Brockschmidt, S. Nowozin, F. Noé,  and R. Tomioka, “Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics,”  (2023), arXiv:2302.01170 [stat.ML] .
  285. F. Noé, S. Olsson, J. Köhler,  and H. Wu, “Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning,” Science 365, eaaw1147 (2019).
  286. M. E. Tuckerman, “Machine learning transforms how microstates are sampled,” Science 365, 982–983 (2019).
  287. L. Klein and F. Noé, “Transferable boltzmann generators,”  (2024), arXiv:2406.14426 [stat.ML] .
  288. J. Köhler, L. Klein,  and F. Noé, “Equivariant flows: exact likelihood generative learning for symmetric densities,” in International conference on machine learning (PMLR, 2020) pp. 5361–5370.
  289. L. I. Midgley, V. Stimper, J. Antorán, E. Mathieu, B. Schölkopf,  and J. M. Hernández-Lobato, “Se(3) equivariant augmented coupling flows,”  (2024), arXiv:2308.10364 [cs.LG] .
  290. V. G. Satorras, E. Hoogeboom, F. B. Fuchs, I. Posner,  and M. Welling, “E(n) equivariant normalizing flows,”  (2022), arXiv:2105.09016 [cs.LG] .
  291. Y. LeCun, S. Chopra, R. Hadsell, M. Ranzato, F. Huang, et al., “A tutorial on energy-based learning,” Predicting structured data 1 (2006).
  292. Y. Song and D. P. Kingma, “How to train your energy-based models,” arXiv preprint arXiv:2101.03288  (2021).
  293. F.-A. Croitoru, V. Hondru, R. T. Ionescu,  and M. Shah, “Diffusion models in vision: A survey,” IEEE Transactions on Pattern Analysis and Machine Intelligence 45, 10850–10869 (2023).
  294. L. Yang, Z. Zhang, Y. Song, S. Hong, R. Xu, Y. Zhao, W. Zhang, B. Cui,  and M.-H. Yang, “Diffusion models: A comprehensive survey of methods and applications,” ACM Computing Surveys 56, 1–39 (2023).
  295. Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon,  and B. Poole, “Score-based generative modeling through stochastic differential equations,”  (2021), arXiv:2011.13456 [cs.LG] .
  296. J. Ho, A. Jain,  and P. Abbeel, “Denoising diffusion probabilistic models,”  (2020), arXiv:2006.11239 [cs.LG] .
  297. M. Arts, V. G. Satorras, C.-W. Huang, D. Zuegner, M. Federici, C. Clementi, F. Noé, R. Pinsler,  and R. van den Berg, “Two for one: Diffusion models and force fields for coarse-grained molecular dynamics,”  (2023), arXiv:2302.00600 [cs.LG] .
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Summary

  • The paper outlines ML/MM hybrid methods that combine fast molecular mechanics with high-accuracy machine learning predictions.
  • It shows that while ML force fields achieve chemical accuracy, they are hindered by computational speed challenges compared to MM methods.
  • The authors propose strategies such as coarse-grained models and optimized tensor frameworks to enable efficient large-scale simulations.

On the Design Space Between Molecular Mechanics and Machine Learning Force Fields

The paper "On the Design Space Between Molecular Mechanics and Machine Learning Force Fields" provides a comprehensive review of the current status, challenges, and future perspectives of force fields, with particular emphasis on the balance between speed and accuracy. The authors argue for the necessity of exploring the vast design space between predominantly accurate but computationally expensive machine learning force fields (MLFFs) and the fast but less accurate molecular mechanics (MM) force fields.

Challenges in Molecular Mechanics Force Fields

Molecular Mechanics force fields have been a workhorse in the computational modeling of biomolecular systems. MM force fields leverage simple functional forms, often harmonic or polynomial, combined with empirical calibrations. These functional forms include contributions from bonds, angles, torsions, Coulomb, and van der Waals interactions. The simplicity of these forms enables MM force fields to achieve linear runtime complexity, making them incredibly fast - a crucial requirement for simulating large biomolecular systems.

However, the traditional MM force fields suffer from limited accuracy, particularly in capturing high-energy regions of the potential energy landscape and intricate quantum mechanical interactions. The paper highlights that the current MM functional forms and their parametrization, often based on human-derived atom typing, restrict the expressiveness and flexibility necessary to cover the extensive chemical and conformational diversity encountered in realistic simulations. While efforts to introduce more sophisticated functional forms (such as higher-order polynomials and coupling terms) exist, the balance between enhancing accuracy and retaining computational efficiency remains challenging.

Advances in Machine Learning Force Fields

On the other hand, MLFFs offer a flexible framework to model complex energy landscapes by utilizing neural networks to approximate ab initio energies and forces. Recent developments in MLFFs have demonstrated accuracy well within the threshold of chemical accuracy (1 kcal/mol), significantly surpassing traditional MM force fields on limited chemical spaces. The paper mentions several state-of-the-art MLFF models that have achieved promising results on benchmark datasets such as MD17, QM9, and SPICE.

Despite their high accuracy, MLFFs are generally hundreds of times slower than MM force fields, which limits their practical applications to large-scale biomolecular simulations. The authors identify speed, stability, and generalizability as the primary bottlenecks for the broader adoption of MLFFs. Ensuring stability, particularly in high-energy and reactive regions, remains a significant hurdle.

Towards a Faster and Accurate Force Field

The authors propose several strategies to bridge the gap between MM and ML force fields. One promising avenue involves the integration of ML techniques with the existing MM frameworks, a method they term "ML/MM hybrid approaches." These approaches aim to combine the best of both worlds by using MLFFs to refine the MM force field parameters and functional forms dynamically. Another potential approach is the development of ultra-fast MLFFs that incorporate physical principles, such as long-range interactions and proper energy conservation laws, to enhance both speed and accuracy.

They also advocate for the use of coarse-grained models and hierarchical frameworks to reduce computational costs while preserving essential physics. These methods involve grouping atoms into "beads" and using ML to determine interactions at a reduced level of detail.

Future Directions

The paper envisions that the next generation of MLFFs will be implemented in highly optimized tensor-accelerating frameworks, which are currently ubiquitous in machine learning and scientific computing. This integration could enable efficient use of automatic differentiation, significantly speeding up force evaluations. Moreover, community-wide efforts to generate high-quality datasets, inclusive of diverse chemical and conformational spaces, are deemed essential for training these force fields.

The authors also mention the concept of foundation models for force fields, drawing parallels from natural language processing and computer vision domains where large models trained on vast amounts of data have shown remarkable success. They suggest that a similar approach could be adopted for creating generalized force fields capable of performing robustly across a wide range of tasks and chemical systems.

Conclusion

In conclusion, the paper by Yuanqing Wang et al. provides an insightful and detailed analysis of the current state and future potential of force fields in computational chemistry. By exploring the design space between MM and ML force fields, the authors highlight the potential for creating faster and more accurate models that can meet the demands of modern biomolecular simulations. The proposed pathways, such as ML/MM hybrid approaches, ultra-fast MLFFs, and community-driven data generation efforts, offer a roadmap for future developments in this area. This work is likely to spur further research aimed at overcoming the limitations of current force field methodologies and harnessing the full potential of machine learning in molecular simulations.

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