符号集成学习实现快速精确的基于物理的原子间势的发现
Symbolic Ensemble Learning Enables Discovery of Fast Accurate Physics-Based Interatomic Potentials
- University of Illinois, Chicago（芝加哥伊利诺伊大学）
- Argonne National Laboratory（阿贡国家实验室）
- Oak Ridge National Laboratory（橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出混合符号-神经框架，结合EAM可解释性与数据驱动学习，通过三种训练协议获得铝的符号模型，并利用加权符号集成构建复合势，超越单个模型精度，实现平衡与非平衡态的稳健预测。
AI中文摘要：
机器学习通过提供具有从头算精度的力场，已经变革了材料模拟，然而在高维回归与物理可解释性之间架起桥梁仍然是一个重大挑战。传统的解析势具有透明性，但往往无法捕捉远离基态区域中的复杂性。在此，我们引入了一个混合符号-神经框架，该框架统一了嵌入原子方法（EAM）的可解释性与数据驱动学习的适应性。使用在密度泛函理论（DFT）数据上训练的方程学习器神经网络（EqNNs），我们通过三种不同的训练协议获得了铝的可解释模型：通过蒙特卡洛树搜索（MCTS）和梯度下降训练的随机初始化，以及两种从铜势初始化的迁移学习策略——一种采用MCTS后接梯度下降，另一种仅使用梯度下降。我们发现，虽然所有三个得到的符号模型都达到了亚10 meV/原子的精度，但它们在函数景观中占据不同的局部最小值，在声子色散、表面能量学和弹性响应方面表现出互补的权衡。通过加权符号集成整合这些多样的函数形式，我们推导出一个复合势，其保真度超过了其组成模型。所得的集成有效地减轻了单个偏差，在状态方程曲率、声子谱和熔化动力学方面提供了与DFT基准的卓越一致性。该方法表明，将迁移学习与集成符号回归相结合，能够产生紧凑、透明的势，能够在平衡和非平衡状态下进行稳健预测。
英文摘要：
Machine learning has transformed materials simulation by delivering force fields with ab initio accuracy, yet bridging the gap between high-dimensional regression and physical interpretability remains a grand challenge. Conventional analytical potentials offer transparency but often fail to capture the complexity of far-from-ground state regimes. Here, we introduce a hybrid symbolic-neural framework that unifies the interpretability of the Embedded Atom Method (EAM) with the adaptability of data-driven learning. Using Equation Learner Neural Networks (EqNNs) trained on density functional theory (DFT) data, we obtain interpretable models for aluminum through three distinct training protocols: random initialization trained via Monte Carlo Tree Search (MCTS) and gradient descent, and two transfer-learning strategies initialized from a copper potential - one employing MCTS followed by gradient descent, and the other using gradient descent only. We find that while all three resulting symbolic models achieve sub-10 meV/atom accuracy, they occupy distinct local minima in the functional landscape, exhibiting complementary trade-offs across phonon dispersion, surface energetics, and elastic response. By integrating these diverse functional forms through a weighted symbolic ensemble, we derive a composite potential that surpasses the fidelity of its constituent models. The resulting ensemble effectively mitigates individual biases, delivering superior consistency with DFT benchmarks across equation-of-state curvature, phonon spectra, and melting dynamics. This approach demonstrates that combining transfer learning with ensemble symbolic regression yields compact, transparent potentials capable of robust prediction across equilibrium and non-equilibrium states.
