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Molecular relaxation by reverse diffusion with time step prediction (2404.10935v2)

Published 16 Apr 2024 in physics.chem-ph, cs.LG, physics.comp-ph, and stat.ML

Abstract: Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.

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Summary

  • The paper introduces MoreRed, demonstrating that reverse diffusion with time step prediction efficiently relaxes molecular structures by learning a pseudo potential energy surface.
  • The method reduces the need for extensive labeled datasets by predicting the noise levels of non-equilibrium inputs.
  • Empirical validation on the QM7-X dataset shows competitive performance against classical force fields and MLFFs, achieving chemical accuracy.

Molecular Relaxation via Reverse Diffusion with Time Step Prediction

Overview of Methodology

MoreRed introduces a novel approach to molecular relaxation through reverse diffusion, named MoreRed (Molecular Relaxation by Reverse diffusion), focusing on denoising non-equilibrium molecular structures by learning a pseudo potential energy surface (PES) rather than the actual physical PES. This approach fundamentally treats the distortions in non-equilibrium structures as noise and employs a generative diffusion model integrated with a newly introduced diffusion time step predictor to determine the level of distortion and thus, the denoising process required.

Key innovations of MoreRed include:

  • Pseudo PES Learning: Instead of learning the complex physical PES, MoreRed learns a simpler pseudo PES which significantly reduces the need for large, labeled training datasets.
  • Diffusion Time Step Prediction: A neural network predicts how far a non-equilibrium structure has diffused from equilibrium, enabling the denoising of inputs with unknown noise levels.
  • Time-invariant structure learning: The method maintains robustness to transformations like rotation and translation, ensuing consistency in predicting molecular structures.

Comparison to Existing Methods

The paper conducts an extensive comparative analysis across multiple fronts:

  • Classical force fields and equivariant neural network force fields, which, while effective, often require extensive labeled data covering a wide chemical diversity.
  • Semi-empirical methods, which provide a computational efficiency advantage but might lack the accuracy provided by machine-learned models. MoreRed is positioned uniquely as it requires only equilibrium structures, devoid of the need for labeling, which is a typical necessity for training machine learning force fields (MLFFs).

Empirical Validation and Results

MoreRed's effectiveness is experimentally validated using the QM7-X dataset involving 42,000 equilibrium structures and 100 associated non-equilibrium structures each, generated via normal-mode displacements. The results are promising:

  • Robustness: MoreRed outperforms classical force fields and demonstrates competitive performance against more advanced MLFF models, especially in data-limited scenarios.
  • Energy Comparison: When comparing the DFT energies of the relaxed structures, MoreRed produces results within chemical accuracy when compared to reference values, although the experimental setup highlighted a potential mismatch in computational settings used in generating dataset labels.

Implications and Future Directions

The adoption of MoreRed can significantly reduce the computational overhead associated with generating expansive labeled datasets in molecular dynamics studies. This efficiency makes it particularly appealing for larger systems or scenarios where data generation is challenging or limited.

The integration of a time step predictor not only enhances the model's adaptability to varying degrees of input distortion but also opens new avenues for refining generative model applications in chemistry and materials science. Future work might explore the extension of MoreRed to dynamic molecular simulations, which would necessitate ongoing advancements in understanding and modeling time-dependent molecular transformations.

Speculations on Future Developments

The potential for MoreRed to be integrated with more dynamic data-driven approaches or hybrid models that combine first-principles methods with machine-learned efficiencies could further enhance its applicability and accuracy. Exploration into adaptive algorithms that dynamically modulate diffusion processes based on real-time data feedback could represent a significant next step in the evolution of molecular simulation technologies.

In summary, MoreRed presents a significant shift towards utilizing generative models for molecular relaxation, emphasizing efficiency and robustness, potentially paving the way for broader applications in computational chemistry and related fields.