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.

该研究使用机器学习潜力提供的Born-Oppenheimer势能表面来预测锡硒化物的粘聚性和热导率，其复杂的功能形式依赖于自动微分，并且使用了一种统一的自动微分方法来获得自动微分梯度，包括力，应力和热通量。

应用自动微分求解压力和热通量