Differentiable Molecular Simulations for Control and Learning

Wujie Wang, Simon Axelrod, Rafael Gómez-Bombarelli

Keywords: Molecular Dynamics, Quantum Dynamics, Differentiable Simulations, Statistical Physics, Machine Learning

Abstract: Molecular simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. Non-quantized molecular behavior is typically simulated with differential equations parameterized by a Hamiltonian, or energy function. TheHamiltonian describes the state of the system and its interactions with the environment. In order to derive predictive microscopic models, one wishes to infer a molecular Hamiltonian from macroscopic quantities. From the perspective of engineering, one wishes to control the Hamiltonian to achieve desired macroscopic quantities. In both cases, the goal is to modify the Hamiltonian such that bulk properties of the simulated system match a given target. We demonstrate how this can be achieved using differentiable simulations where bulk target observables and simulation outcomes can be analytically differentiated with respect to Hamiltonians. Our work opens up new routes for parameterizing Hamiltonians to infer macroscopic models and develops control protocols

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2003.00868/code)