[论文解读] End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems

Linfeng Zhang, Jiequn Han+4 more|arXiv (Cornell University)|May 23, 2018

Machine Learning in Materials Science参考文献 30被引用 155

一句话总结

DeepPot-SE 是一个端到端、保持对称性的神经网络势能面（PES），具备大小可扩展性、可微分性，并且可扩展，能够以接近从头计算方法的精度描述有限分子与扩展材料。

ABSTRACT

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES for a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity.

研究动机与目标

• Develop an end-to-end ML-based potential energy surface (PES) that approaches quantum-mechanical accuracy for both finite and extended systems.
• Ensure the model input relies only on atomic species and coordinates, while preserving translational, rotational, and permutational symmetries.
• Achieve size-extensivity and smoothness suitable for molecular dynamics, with linear scaling in system size.
• Provide a unified framework applicable to diverse systems (organic molecules, metals, semiconductors, insulators, HEAs).
• Release open-source code and data to facilitate adoption and benchmarking.

提出的方法

• Decompose total energy as a sum of atomic energies, E = sum_i E_i, with atom-type dependent sub-networks.
• Define local environments within a cut-off radius r_c and map relative coordinates to generalized coordinates tilde R^i with a differentiable weighting s(r_ji).
• Construct symmetry-preserving embeddings G^i from the local environment and use them to form a symmetry-preserving feature matrix D^i = (G^{i1})^T tilde R^i (tilde R^i)^T G^{i2} that serves as input to the atomic energy network.
• Use an encoding network to produce coordinate/chemical filters that preserve rotation and permutation symmetry, followed by a fitting network to output E_i; sum over i to obtain E.
• Train end-to-end with Adam, using a loss that combines energy, forces, and virial (when available) to enforce energy and force consistency.
• Data are drawn from DFT/CP2K molecular dynamics trajectories across diverse systems, enabling a single model to generalize across finite and extended regimes.

实验结果

研究问题

• RQ1 Can an end-to-end, symmetry-preserving ML model accurately describe PESs for both finite systems and extended materials?
• RQ2 How does DeepPot-SE perform across metals, semiconductors, insulators, and multi-component/high-entropy alloys compared to other ML PES approaches?
• RQ3 Does the model maintain extensivity, differentiability, and symmetry properties while enabling scalable training and inference?
• RQ4 What is the impact of including forces and virials in training on data efficiency and accuracy?
• RQ5 Is a unified model feasible for multiple chemical families (e.g., C/H/O/N) versus separate per-subsystem models?

主要发现

• The DeepPot-SE framework yields accurate energies and forces across a wide range of systems, including small molecules and bulk materials, using a single end-to-end model.
• The method preserves translational, rotational, and permutational symmetries and scales linearly with system size due to the local environment and energy decomposition.
• Compared to other ML PES approaches, DeepPot-SE demonstrates competitive or superior performance on representative systems such as Cu, Ge, Si, TiO2 polymorphs, pyridine polymorphs, MoS2 with Pt clusters, and a CoCrFeMnNi high-entropy alloy.
• The training scheme benefits from including both energy and force information, improving data efficiency and model fidelity.
• The approach provides an open-source implementation (DeePMD-kit) and data resources for benchmarking across diverse materials.