Foundation MLPs: Concepts & Advances

• Foundation MLPs are atomistic energy models trained on diverse quantum datasets to capture potential-energy surfaces with near first-principles accuracy.
• They combine local energy decomposition with advanced deep learning architectures, physical priors, and transfer learning techniques for broad reuse across tasks.
• They integrate robust software ecosystems and deployment-aware validation, ensuring scalability, interoperability, and reliable performance in simulations.

Searching arXiv for papers on foundation machine learning potentials and related atomistic MLIPs. Foundation machine learning potentials (MLPs), often called foundation machine learning interatomic potentials (MLIPs), are broadly pretrained atomistic models intended to represent potential-energy surfaces across wide regions of chemical, structural, and thermodynamic space, rather than being fit only to a single material, molecule, or narrowly defined simulation regime. In the atomistic setting, they extend the standard MLP objective—learning energies and forces with near first-principles fidelity—to a regime of reuse, transfer, interoperability, and downstream adaptation across tasks, chemistries, and simulation workflows. The contemporary literature does not define a single canonical architecture or training recipe for such models. Instead, the concept emerges from several converging lines of work: broad-coverage local energy models and active-learning pipelines in materials science (Wen et al., 2022, Mishin, 2021), meta-learning over heterogeneous quantum-mechanical datasets (Allen et al., 2023), software and deployment frameworks for multi-backend interoperability (Zeng et al., 26 Feb 2025), compositional generalization across alloy spaces (Sheriff et al., 14 Jun 2025, Liu et al., 19 Oct 2025, Song et al., 2023), transfer learning across related chemistries (Röcken et al., 19 Feb 2025), physically richer models with explicit electrostatics or charge equilibration (Ko et al., 2023, Kocer et al., 2024), deployment-aware evaluation for free energies and simulation tasks (&&&10&&&, Ge et al., 2024), and, more recently, common latent-space analyses of independently trained foundation MLIPs (Li et al., 5 Dec 2025).

1. Concept and scope

Foundation MLPs are atomistic energy models trained on large and chemically diverse datasets so that a single pretrained model, or a tightly related model family, can be reused across many downstream simulations. In the broad materials-science view, interatomic potentials provide the total energy $E$ as a function of atomic positions, with forces obtained from energy gradients, $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$ (Mishin, 2021). Most modern short-range formulations decompose the total energy into local atomic contributions, $E = \sum_i E_i$, which underlies the scalability of both classical and machine-learned interatomic models (Mishin, 2021, Wen et al., 2022).

The foundation perspective extends this local-potential paradigm from system-specific fitting to broad reuse. Deep Potential (DP) methods illustrate this transition at the ecosystem level: the review of DPs presents them not only as local many-body potentials trained to energies, forces, and virials, but also as a software and data ecosystem comprising DeePMD-kit, DP-GEN, dpdata, Autotest, and the DP Library (Wen et al., 2022). In that framing, what is “foundation-like” is not merely the architecture, but the combination of a general-purpose formalism, large-scale data generation, reusable trained models, and deployment into production simulation workflows (Wen et al., 2022).

A closely related conceptual distinction is between special-purpose and general-purpose potentials. The review of machine-learning interatomic potentials for materials science emphasizes that MLPs are fundamentally interpolators over quantum-mechanical databases, with transferability governed by the breadth of the training domain rather than by a compact physics-based ansatz (Mishin, 2021). Foundation MLPs can therefore be understood as an attempt to make as much of practical atomistic simulation as possible fall into an interpolation regime through scale, diversity, and transferable representations. The literature surveyed here supports this idea, but also shows that present systems remain domain-bounded: metallic alloy models such as UNEP-v1 cover 16 elemental metals and their alloys rather than all bonding classes (Song et al., 2023), while molecular meta-learning studies remain centered on CHNO organic chemistry (Allen et al., 2023).

2. Representations, architectures, and physical priors

The modern architectural landscape for foundation MLPs spans descriptor-based local models, deep local-coordinate models, graph neural networks, equivariant message-passing architectures, and charge-aware or electrostatically augmented formulations. The review of neural network potentials organizes these methods into “generations”: first-generation low-dimensional PES fits; second-generation local high-dimensional models based on atomic energy decompositions; third-generation models with explicit long-range electrostatics; and fourth-generation models capable of non-local charge transfer and global electronic dependence (Kocer et al., 2021). This taxonomy remains highly relevant to foundation MLPs because broad transfer across molecules, solids, interfaces, and charged systems cannot be achieved by locality alone (Kocer et al., 2021).

Descriptor-based models remain important because they encode symmetry exactly and scale well. High-dimensional neural network potentials use atom-centered symmetry functions, while Deep Potential models use local environment matrices and symmetry-preserving descriptor constructions (Wen et al., 2022, Tokita et al., 2023). Descriptor incompleteness and combinatorial growth with the number of elements are recognized limitations for broad chemistry (Kocer et al., 2021). Learned representations, especially message-passing and equivariant architectures, address these limits by constructing task-adaptive geometric embeddings from positions and species (Kocer et al., 2021). The solvation review identifies NequIP, MACE, PaiNN, Allegro, SO3krates, ViSNet, and related equivariant GNNs as especially promising for directional interactions and tensorial response, while also emphasizing that long-range electrostatics and charge transfer often require additional inductive bias beyond local equivariance (Banchode et al., 28 May 2025).

Deep Potential models occupy a central position because they combine locality, differentiable energy-based training, and high-performance deployment. Their standard supervised loss jointly fits energies, forces, and virials (Wen et al., 2022). The review explicitly gives

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$

with separate energy, force, and virial terms (Wen et al., 2022). This multitarget structure foreshadows later foundation-style multitask supervision, where energies, forces, charges, dipoles, virials, or response properties are trained jointly (Banchode et al., 28 May 2025).

Physical priors re-enter the field in several forms. The 2021 review on machine-learning interatomic potentials distinguishes a third class of “physically-informed ML potentials,” in which ML predicts environment-dependent parameters of a physics-based interaction model rather than mapping directly from descriptors to energy (Mishin, 2021). The physically informed neural network (PINN) is the main example there, using a bond-order potential as the analytic scaffold and a neural network to predict local parameters (Mishin, 2021). This line of thought is continuous with later charge-aware fourth-generation models (Ko et al., 2023, Kocer et al., 2024) and with electrostatically responsive student models distilled from broad foundation MLIPs (Wang et al., 12 Jun 2026).

3. Training regimes: broad pretraining, active learning, meta-learning, and transfer

The literature supports several distinct training paradigms relevant to foundation MLPs.

The first is broad supervised fitting to large quantum-mechanical datasets. DP methods exemplify this paradigm in materials science, pairing local many-body networks with active-learning-based concurrent learning in DP-GEN (Wen et al., 2022). DP-GEN iteratively trains an ensemble, explores configuration space, estimates model deviation through force disagreement, labels selected configurations with DFT, and retrains (Wen et al., 2022). The review gives the model-deviation indicator

$$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$

with the ensemble mean force defined over $N_m$ models (Wen et al., 2022). This makes active learning part of the foundation pipeline rather than an afterthought.

A second paradigm is meta-learning over heterogeneous tasks. “Learning Together: Towards foundational models for machine learning interatomic potentials with meta-learning” explicitly proposes Reptile-based meta-learning as a route to pretrained or “foundational” MLIPs when the available data come from inconsistent quantum-mechanical levels of theory (Allen et al., 2023). The central idea is to treat each dataset or level of theory as a separate task, and to learn an initialization that can be quickly specialized to a new task with limited data (Allen et al., 2023). The work uses ANI as the base learner and shows that, for aspirin, force RMSE improves from $5.35 \pm 0.41$ kcal/mol/Å without pretraining to $3.38 \pm 0.16$ kcal/mol/Å with $k=1$ joint training, with further improvement for larger $k$ (Allen et al., 2023). In the ANI-1x/ANI-1ccx case, meta-learning yields $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$0 kcal/mol relative to $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$1 kcal/mol for joint training, although direct transfer from a closely matched single source performs even better at $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$2 or $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$3 kcal/mol (Allen et al., 2023). This caveat is central: foundation-style pretraining is not automatically superior to narrow transfer when source and target are extremely close.

A third paradigm is direct transfer learning across related chemical systems. “Enhancing Machine Learning Potentials through Transfer Learning across Chemical Elements” studies Si $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$4 Ge transfer using DimeNet++ and shows that transfer learning across chemically similar elements improves force prediction, temperature transferability, and MD stability, especially in data-scarce regimes (Röcken et al., 19 Feb 2025). The model is trained only on forces, with the force-matching loss

$$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$5

as reported in the source material (Röcken et al., 19 Feb 2025). All network parameters, including atom embeddings, are transferred and then fully fine-tuned rather than frozen (Röcken et al., 19 Feb 2025). The study is narrow by design, but it directly supports the claim that reusable atomistic knowledge can be encoded in pretrained interatomic models and then adapted to nearby chemistry.

A fourth regime is distillation from large pretrained teachers. “Distilling latent electrostatics from foundation machine learning interatomic potentials” uses teacher predictions from broad foundation MLIPs to train lightweight student models augmented with Latent Ewald Summation (LES), thereby extracting latent electrostatic response and producing efficient electrically responsive models (Wang et al., 12 Jun 2026). The paper frames foundation MLIPs as models “trained on large datasets across broad configurational and compositional spaces” and uses teachers including UMA, MACE, Orb, eSEN, GemNet-OC, PET, and EquiformerV2-based models (Wang et al., 12 Jun 2026). This suggests a layered ecosystem in which large foundation teachers and smaller deployment-oriented students coexist.

4. Data coverage, compositional transfer, and alloy-space generalization

A central question for foundation MLPs is whether broad compositional and structural transfer can be engineered through data design rather than only architecture. The alloy literature gives some of the clearest evidence.

UNEP-v1 presents a unified potential for 16 elemental metals and their alloys, using a local NEP4 architecture with pair-dependent descriptor coefficients and species-specific atomic networks (Song et al., 2023). The total energy is

$$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$6

and the per-atom model is expressed as

$$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$7

where $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$8 is the central species and $$\mathbf{F}_i = -\frac{\partial E}{\partial \mathbf{r}_i}$$9 indexes neighbor species (Song et al., 2023). The training dataset contains only unary and binary systems, yet the authors argue through PCA in descriptor space and extensive testing that this suffices to cover multicomponent metallic alloys (Song et al., 2023). Final training uses 105,464 structures and 6,886,241 atoms, labeled with VASP/PBE, at a reported DFT cost of about six million CPU hours (Song et al., 2023). On public test sets with up to 13 components, force RMSEs are 76, 196, and 269 meV/Å depending on the benchmark, and formation-energy MAEs are 75 meV/atom on Materials Project ternaries and 60 meV/atom on GNoME, far below the reported EAM baseline (Song et al., 2023).

A closely related line of work makes the data-design argument more explicit. “Machine learning potentials for modeling alloys across compositions” introduces motif-based sampling (MBS) as an information-theoretic way to balance local chemical motifs in alloy datasets (Sheriff et al., 14 Jun 2025). The paper argues that compositional generalization is limited less by model expressivity than by inadequate sampling of the local chemical environments that arise as composition and order vary (Sheriff et al., 14 Jun 2025). Using Jensen–Shannon divergence and motif packing density, the authors show that MBS improves training-set coverage of local environments. In one 702-configuration dataset, the Jensen–Shannon divergence drops from $E = \sum_i E_i$0 bits to $E = \sum_i E_i$1 bits and motif packing density rises by 38% to 72.3% of all possible motifs (Sheriff et al., 14 Jun 2025). The resulting models reproduce stacking-fault energies, short-range order, heat capacities, and phase diagrams across AuPt, CuAu, CrCoNi, and TiTaVW, with extensive experimental comparison (Sheriff et al., 14 Jun 2025). This supports a general principle for foundation MLPs: the relevant unit of diversity is not always global composition, but often the local environment distribution.

“Efficient small-cell sampling for machine-learning potentials of multi-principal element alloys” advances a related but distinct claim: for metallic multi-principal element alloys, diverse unary and binary small-cell structures may suffice to span the local environments needed for many-element systems (Liu et al., 19 Oct 2025). The small-cell sampling (SCS) protocol enumerates symmetry-inequivalent unary and binary BCC-, FCC-, and HCP-like cells of 4, 8, and 12 atoms, adds near-hull binary compounds from Materials Project, perturbs lattice and positions, and then labels the resulting structures with VASP/PBE (Liu et al., 19 Oct 2025). In TiZrHfCuNi, the best MTP trained only on unary/binary small cells achieves validation errors of 16.8 meV/atom, 132.1 meV/Å, and 0.68 GPa on a held-out set of 2,298 large-cell multicomponent structures, including ternary, quaternary, quinary, and intermetallic configurations (Liu et al., 19 Oct 2025). The same strategy is then used to model phase transformation in TiZrVMo, chemical ordering in CoCrFeMnNi, and thermodynamics in AlTiZrNbHfTa (Liu et al., 19 Oct 2025). Together with UNEP-v1 (Song et al., 2023), this provides one of the strongest current demonstrations of domain-specific foundation behavior in metallic systems.

5. Electrostatics, charge transfer, and fourth-generation models

A purely local foundation MLP cannot be fully general in systems where the relevant state variables are electronic and nonlocal. Several papers in the corpus make this point explicitly.

“Accurate Fourth-Generation Machine Learning Potentials by Electrostatic Embedding” introduces the electrostatically embedded fourth-generation high-dimensional neural network potential (ee4G-HDNNP) (Ko et al., 2023). The total energy is

$E = \sum_i E_i$2

where charges $E = \sum_i E_i$3 are determined by a global charge equilibration step and the short-range atomic energy networks receive not only structural descriptors and the central atom charge, but also element-resolved local electrostatic potentials $E = \sum_i E_i$4 (Ko et al., 2023). The charge-equilibration functional is

$E = \sum_i E_i$5

with charges solved under the global constraint $E = \sum_i E_i$6 (Ko et al., 2023). The paper argues that electrostatic embedding improves transferability and helps resolve degeneracies that remain even in earlier fourth-generation models (Ko et al., 2023).

“Machine learning potentials for redox chemistry in solution” applies the fourth-generation HDNNP concept to aqueous FeCl$E = \sum_i E_i$7 and FeCl$E = \sum_i E_i$8, showing directly that standard second-generation local MLPs cannot reliably determine oxidation state from local geometry alone (Kocer et al., 2024). The second-generation model uses the standard local atomic-energy sum

$E = \sum_i E_i$9

while the fourth-generation model is

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$0

The crucial point is that charges in the 4G model are determined by global charge equilibration and then fed back into the short-range energy model, allowing the potential to infer Fe$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$1 versus Fe$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$2 from the number of chloride counterions in the periodic cell, even when those counterions are outside any local cutoff (Kocer et al., 2024). The 2G and 4G models have similarly low energy and force RMSEs—for example 0.262/0.271 meV/atom and 0.034/0.035 eV/Bohr for the combined 2G train/test set, versus 0.258/0.273 meV/atom and 0.033/0.033 eV/Bohr for the combined 4G model—but only the 4G model yields the correct oxidation-state-dependent Fe–O radial distribution functions in large boxes (Kocer et al., 2024). This is an unusually sharp illustration that conventional energy/force errors can obscure a fundamental representational failure.

The broader implication for foundation MLPs is that support for charge transfer, redox chemistry, ionic systems, or electrically responsive interfaces requires explicit global electronic-state mechanisms rather than broader local training data alone. The 2021 review of neural network potentials had already framed this need through its third- and fourth-generation taxonomy (Kocer et al., 2021), and the 2025 review on solvation modeling similarly emphasizes that long-range polarization, dielectric screening, and charge transfer are central obstacles in solvated systems (Banchode et al., 28 May 2025). The emerging consensus is therefore architectural: nonlocal charge models, electrostatic augmentation, or related global-state constructions are likely necessary components of broadly general reactive foundation MLPs.

6. Software ecosystems, interoperability, and deployment

Foundation MLPs are not only models but also infrastructure. DeePMD-kit v3 is the clearest software-focused contribution in this direction. “DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning Potentials” presents a pluggable multi-backend framework supporting TensorFlow, PyTorch, JAX, PaddlePaddle, and a reference “DP” backend based on the Array API (Zeng et al., 26 Feb 2025). The architecture preserves the existing Python and C/C++ APIs while enabling backend switching, model conversion, plugin integration, and deployment continuity into LAMMPS, i-PI, AMBER, CP2K, OpenMM, GROMACS, ASE, ABACUS, and related environments (Zeng et al., 26 Feb 2025). This is highly relevant to foundation MLPs because large pretrained models are valuable only if they can be trained, serialized, converted, and deployed across ecosystems without major friction.

The review of DPs also emphasizes the role of data and model repositories. The DP Library stores trained potentials, training datasets, and electronic-structure settings, thereby supporting reuse, extension, and reproducibility (Wen et al., 2022). This repository-driven model is a practical analogue of the checkpoint culture around foundation models in language and vision.

Interoperability has also become a representational question. “Platonic representation of foundation machine learning interatomic potentials” studies seven independently developed foundation MLIPs and argues that, although their raw latent spaces are model-specific, they exhibit a common statistical geometry after projection relative to shared atomic anchors (Li et al., 5 Dec 2025). The anchor-relative representation is

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$3

and is used to compare MACE, Orb, SevenNet, and related models in a unified metric space (Li et al., 5 Dec 2025). Quantitative comparison uses Procrustes similarity, mutual $$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$4-nearest-neighbor overlap, and entropic optimal transport, combined into a composite “SuperScore”

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$5

The paper reports global alignment scores $$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$6 within the MACE family, low local-neighborhood agreement across distant model families, periodic-table-like organization in mean-pooled element embeddings, and the ability to detect representational failure modes such as symmetry breaking and incorrect phonon dispersions (Li et al., 5 Dec 2025). This suggests that future foundation MLP ecosystems may require not only interoperable file formats and software backends, but also interoperable representational interfaces.

7. Evaluation beyond RMSE: simulation-oriented and deployment-aware assessment

A recurring theme in the literature is that pointwise energy and force error are insufficient to certify a foundation MLP. Several papers make this case from complementary directions.

“Tell machine learning potentials what they are needed for: Simulation-oriented training exemplified for glycine” shows that test-set RMSE on a standard random split can correlate only weakly with actual simulation performance (Ge et al., 2024). The paper trains ANI-type models on a global glycine PES with 70,099 B3LYP/aug-cc-pVDZ energies and gradients, and introduces an energy-based weighting function

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$7

to emphasize low-energy structures (Ge et al., 2024). The combined loss is

$$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$8

with weighted energy and gradient terms (Ge et al., 2024). The key result is that models with worse test RMSE can have dramatically better conformer energies, transition-state energies, frequencies, and zero-point energies. For example, the best simulation-oriented ANI has minima MAE 0.016 kcal/mol and transition-state MAE 0.039 kcal/mol with test RMSE 0.45 kcal/mol, whereas off-the-shelf ANI has minima MAE $$\mathcal L = \frac{1}{|\mathcal B|}\sum_{k\in \mathcal B} \left( p_e \mathcal L_e^{(k)} + p_f \mathcal L_f^{(k)} + p_v \mathcal L_v^{(k)} \right),$$9, transition-state MAE $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$0, and better RMSE $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$1 kcal/mol (Ge et al., 2024). This is a direct warning against equating benchmark RMSE with downstream usefulness.

“Considerations in the use of ML interaction potentials for free energy calculations” makes the same point in a dynamics-and-thermodynamics setting using Allegro on butane and alanine dipeptide (ADP) (Mendible et al., 2024). The model is trained jointly on energies and forces with local equivariant features, but the paper finds that low framewise energy and force MAEs do not guarantee accurate free-energy surfaces. For butane, even models with energy MAEs around 0.002–0.010 kcal/mol and force MAEs around 0.012–0.043 kcal/(mol Å) can fail badly if training data omit the relevant high-free-energy regions; free-energy MAE jumps from about 0.07–0.09 kcal/mol for minima-inclusive training to about 0.45–0.47 kcal/mol when trained only on the global minimum basin (Mendible et al., 2024). For ADP, even the best static ab initio model, with energy MAE 0.115 kcal/mol and force MAE 0.233 kcal/(mol Å), still yields a projected free-energy MAE of 2.59 kcal/mol and fails to recover the free-energy surface acceptably (Mendible et al., 2024). The review of solvation modeling reaches a similar conclusion more broadly: physically meaningful evaluation must include free energies, solvent structure, interfacial observables, response properties, and stability under rollout, not only label-wise errors (Banchode et al., 28 May 2025).

These studies imply that foundation MLPs require deployment-aware validation. A model intended for rare-event sampling, free energies, redox chemistry, or interfacial spectroscopy must be evaluated in those regimes. Otherwise, the breadth implied by “foundation” remains nominal.

8. Solvation, biomolecular, and multiscale directions

The move toward foundation MLPs is particularly demanding in molecular solvation and biomolecular simulation, where broad transfer requires simultaneous treatment of local chemistry, explicit solvent structure, long-range polarization, and multiple scales.

“Machine-Learned Potentials for Solvation Modeling” provides the clearest recent synthesis of these issues (Banchode et al., 28 May 2025). The review presents a general supervised-learning formulation with energy-only, force-only, and combined losses: $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$2

$$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$3

$$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$4

and emphasizes that explicit solvent, interfacial, and reactive environments expose the limitations of local short-range MLPs (Banchode et al., 28 May 2025). The review highlights charge-aware models such as CENT, QeqNN, and QRNN, hybrid explicit/implicit workflows, $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$5-learning, and active learning as central design patterns for future transferable solvation-aware MLPs (Banchode et al., 28 May 2025). It also explicitly identifies transformer-based pretraining, generative models, and latent-space alignment as future directions (Banchode et al., 28 May 2025). In that sense, the paper is foundation-oriented in diagnosis if not yet in solution.

A biomolecular perspective reaches a related conclusion from a different angle. “Machine Learning Potentials: A Roadmap Toward Next-Generation Biomolecular Simulations” frames MLPs as a unifying framework across scales, from quantum chemistry to atomistic molecular mechanics to coarse-grained models (Fabritiis, 2024). The paper emphasizes that biomolecular applications demand millisecond-scale trajectories, sub-millisecond step evaluation, and accurate treatment of long-range electrostatics in heterogeneous environments such as membrane proteins and solvated complexes (Fabritiis, 2024). It argues that the first practical impact is likely to come from hybrid NNP/MM schemes for protein–ligand binding, with the ligand treated by an MLP and the environment by classical MM (Fabritiis, 2024). This is a notable counterpoint to the most ambitious foundation narratives: in biomolecular simulation, hardware efficiency, stability, and hybridization may matter more than maximizing benchmark accuracy on atomistic micro-datasets.

9. Distillation, response properties, and the teacher–student foundation stack

One emerging direction is to use large foundation MLIPs as teachers that can be probed, distilled, or specialized. The LES-based distillation paper is the clearest example (Wang et al., 12 Jun 2026). The student energy is written as

$$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$6

where $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$7 is produced by a lightweight local MLP backbone and $$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$8 is an Ewald-type electrostatic term based on latent charges (Wang et al., 12 Jun 2026). The reciprocal-space polarization is

$$\epsilon_t = \max_i \sqrt{ \left\langle \left\| \mathbf F_{w,i}(\mathcal R_t) - \left\langle \mathbf F_{w,i}(\mathcal R_t)\right\rangle \right\|^2 \right\rangle },$$9

and the Born effective charge tensor is obtained in the long-wavelength limit as

$N_m$0

The paper shows that distilled student models can recover Born effective charges and infrared spectra from teacher energies and forces alone, and that the underlying DFT level and training dataset often matter more than the teacher architecture in determining electrostatic and spectroscopic quality (Wang et al., 12 Jun 2026). For liquid water, BEC RMSE in distilled students drops from about 0.10 $N_m$1 to 0.05 $N_m$2 with only 25 configurations, and $N_m$3 rises to about 0.98 (Wang et al., 12 Jun 2026). This supports a teacher–student view of foundation MLPs in which large general models store latent physical information that can be extracted into cheaper, system-specific, or electrically responsive surrogates.

10. Limits, controversies, and open problems

The surveyed literature is broadly optimistic about foundation MLPs, but it also delineates their current limits with unusual clarity.

One persistent issue is transferability versus proximity. The meta-learning study shows that heterogeneous multi-fidelity pretraining is beneficial when source tasks are diverse and downstream data are scarce, but that a single closely matched source can still beat broader meta-pretraining in some cases (Allen et al., 2023). The Si $N_m$4 Ge transfer study likewise shows that transfer can have beneficial but also adversarial effects on out-of-target properties (Röcken et al., 19 Feb 2025). This suggests that “more pretraining” is not an unconditional monotone.

A second issue is locality versus global physics. Fourth-generation HDNNPs, electrostatic embedding, and redox-capable 4G models all exist because standard local atomic-energy models fail in globally constrained charge environments (Ko et al., 2023, Kocer et al., 2024). The solvation review reaches the same conclusion for explicit solvent and ionic systems (Banchode et al., 28 May 2025). A plausible implication is that future foundation MLPs will require a layered representation: local equivariant geometry plus global electronic state variables or long-range field mechanisms.

A third issue is evaluation mismatch. Glycine, butane, and ADP all demonstrate that random test splits and standard RMSEs can be profoundly misleading for actual simulation tasks (Ge et al., 2024, Mendible et al., 2024). A foundation MLP benchmark suite that ignores rollout stability, free-energy fidelity, rare-event coverage, redox-state correctness, or spectroscopy is therefore incomplete.

A fourth issue is software and ecosystem fragmentation. DeePMD-kit v3 addresses this directly by turning a formerly TensorFlow-centered package into a multi-backend interoperable platform (Zeng et al., 26 Feb 2025). Yet the need for backend-neutral APIs, conversion tools, unchanged MD interfaces, and standardized serialization implies that infrastructure remains a major component of the foundation problem.

A fifth issue is interpretability and cross-model comparison. The Platonic-representation study suggests that independently trained foundation MLIPs may share a common statistical geometry, but only at a coarse scale; local neighborhood structure remains divergent and subtle structural distinctions such as polymorph differences are not consistently aligned after simple pooling (Li et al., 5 Dec 2025). This indicates that latent-space interoperability is promising but still partial.

Finally, a domain-boundary issue remains. Some of the strongest present evidence for foundation behavior comes from metallic alloys (Song et al., 2023, Sheriff et al., 14 Jun 2025, Liu et al., 19 Oct 2025), where locality and pair-parameterized chemistry are favorable. Extending that level of compositional transfer to charged systems, oxides, molecular liquids, biomolecules, or reactive interfaces remains an open problem.

11. Outlook

The current literature suggests that foundation MLPs are best understood not as a single architecture, but as a research program combining broad quantum-mechanical pretraining, active and task-aware data acquisition, physically informed inductive bias, software interoperability, and downstream adaptation. Broad local energy models and ecosystems such as DP provide the materials-science backbone (Wen et al., 2022). Meta-learning and transfer learning show how heterogeneous data and chemically related sources can be turned into reusable priors (Allen et al., 2023, Röcken et al., 19 Feb 2025). Alloy studies demonstrate that careful representation and data design can yield genuine compositional transfer within a domain (Song et al., 2023, Sheriff et al., 14 Jun 2025, Liu et al., 19 Oct 2025). Fourth-generation and electrostatically embedded models show that nonlocal charge physics must be elevated from a correction to a core representational variable in redox and solvated regimes (Ko et al., 2023, Kocer et al., 2024). Deployment-focused work on free energies and simulation-oriented training warns that no foundation claim is credible without workflow-level validation (Mendible et al., 2024, Ge et al., 2024). Multi-backend infrastructure and latent-space interoperability indicate that the field is beginning to think beyond isolated models toward a connected ecosystem of pretrained atomistic representations (Zeng et al., 26 Feb 2025, Li et al., 5 Dec 2025).

This suggests that the mature form of a foundation MLP will likely be neither a purely local graph network nor a single monolithic universal checkpoint. A more plausible near-term endpoint is a stack of interoperable pretrained atomistic models, teacher–student distillation routes, charge-aware or electrostatically responsive variants, task-specific fine-tuning or meta-adaptation, and benchmark suites defined by simulation objectives rather than only by held-out label error.