Differentiable Molecular Simulations for Control and Learning (2003.00868v2)

Abstract: Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is typically simulated with differential equations parameterized by a Hamiltonian, or energy function. The Hamiltonian 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 that agrees with observed macroscopic quantities. From the perspective of engineering, one wishes to control the Hamiltonian to achieve desired simulation outcomes and structures, as in self-assembly and optical control, to then realize systems with the desired Hamiltonian in the lab. In both cases, the goal is to modify the Hamiltonian such that emergent 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, opening up new routes for parameterizing Hamiltonians to infer macroscopic models and develop control protocols.

• The paper introduces a differentiable simulation framework that leverages automatic differentiation to optimize molecular Hamiltonians.
• It demonstrates the use of graph neural networks to steer particle dynamics and guide polymer folding processes through learned bias potentials.
• The method establishes precise control protocols for both classical and quantum dynamics, potentially revolutionizing material design and molecular engineering.

Differentiable Molecular Simulations for Control and Learning: A Technical Overview

The paper "Differentiable Molecular Simulations for Control and Learning," authored by Wujie Wang, Simon Axelrod, and Rafael Gómez-Bombarelli, offers a comprehensive framework for applying differentiable simulations to molecular systems. This approach leverages the ability to analytically differentiate observables with respect to system Hamiltonians, thereby facilitating the parameterization of Hamiltonians and the development of control protocols. The work is primarily affiliated with the Massachusetts Institute of Technology (MIT) and Harvard University.

Summary of Key Concepts

At a fundamental level, molecular dynamics (MD) simulations are employed to understand microscale molecular processes and engineer macroscopic material behavior. Traditional simulations use differential equations derived from Hamiltonians to describe system states and interactions. The authors aim to enhance MD simulations by introducing differentiable simulations, wherein derivatives of simulation results with respect to Hamiltonians can be directly computed. This ability opens new opportunities for inferring microscopic models and designing control protocols, particularly in environments with specified thermodynamic conditions.

Differentiable Simulations

The novel aspect of this work is the integration of differentiable simulations, achieved through automatic differentiation. The use of adjoint sensitivity methods allows for the backpropagation of output position and momentum derivatives, using reverse-mode differentiation to maintain computational efficiency.

A key application explored is the adaptation of differentiable simulations to control Hamiltonians via graph neural networks (GNNs), thereby enabling control over macroscopic system states from microscopic parameters. This is exemplified by controlling particle dynamics in two-dimensional and three-dimensional systems to achieve desired configurations through learned bias potentials.

Targeted Molecular Dynamics

The paper further demonstrates the utility of differentiable simulations in steering molecular systems towards target states. This is achieved by perturbatively adjusting Hamiltonians to encourage transitions between specific states, bypassing the need for predefined reaction coordinates. The method is validated through simulations of polymer folding processes, emphasizing the potential for GNNs to model complex molecular energies.

Learning and Control Protocols

A distinctive feature of this research is the formulation of control protocols for quantum dynamics influenced by external fields. The authors apply their framework to model retinal isomerization, optimizing the quantum yield via electric field adjustments. The capability to shape control protocols through automatic differentiation of simulation trajectories indicates a significant step towards real-time modulation of complex quantum systems.

Implications and Future Directions

The methodology proposed in this work could revolutionize molecular simulations by enhancing control over material properties and dynamics. In practical terms, this could lead to more efficient pathway exploration in complex systems, improved material design, and the development of advanced non-equilibrium simulation techniques. Moreover, the fusion of machine learning with molecular physics simulation underscores a trend towards more integrated, data-driven approaches in computational chemistry and materials science.

Future directions for this research include the application of differentiable simulations to a broader range of molecular systems, incorporating diverse boundary conditions and control scenarios. Advances in computational frameworks for differential equations could further enhance the scalability and efficiency of these simulations, offering insights into even more complex and larger-scale systems.

In conclusion, the paper presents a robust approach to molecular simulation, tying together differentiable computing and molecular dynamics to push the boundaries of current methodologies in material science and engineering. By bridging the gap between macroscopic observables and microscopic control, this research lays the groundwork for innovative applications in molecular engineering and beyond.