Machine-learning potentials provide computationally efficient and accurate approximations of the Born-Oppenheimer potential energy surface. This potential determines many materials properties and simulation techniques usually require its gradients, in particular forces and stress for molecular dynamics, and heat flux for thermal transport properties. Recently developed potentials feature high body order and can include equivariant semi-local interactions through message-passing mechanisms. Due to their complex functional forms, they rely on automatic differentiation (AD), overcoming the need for manual implementations or finite-difference schemes to evaluate gradients. This study demonstrates a unified AD approach to obtain forces, stress, and heat flux for such potentials, and provides a model-independent implementation. The method is tested on the Lennard-Jones potential, and then applied to predict cohesive properties and thermal conductivity of tin selenide using an equivariant message-passing neural network potential.

翻译：摘要：机器学习势能函数能够以高效且准确的方式近似描述Born-Oppenheimer势能面。该势能决定了众多材料性质，而相应的模拟技术通常需要获取其梯度信息，特别是分子动力学模拟所需的原子受力与应力张量，以及热输运性质研究中的热通量。近年来发展的势能函数具有高阶体态特征，能够通过消息传递机制包含等变半局域相互作用。由于这些势能函数具有复杂的函数形式，其梯度求解需依赖自动微分技术，从而避免了人工推导和有限差分方法的局限性。本研究提出了一种统一的自动微分框架，可同时获得此类势能函数对应的原子受力、应力张量和热通量，并给出了与模型无关的实现方案。该方法首先在Lennard-Jones势能体系中进行验证，随后应用于基于等变消息传递神经网络势能预测硒化锡的凝聚态性质与热导率。