Petix C Levi, Fakhraei Mohammadreza, Kieslich Chris A, Howard Michael P
Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States.
J Chem Theory Comput. 2024 Feb 27;20(4):1538-1546. doi: 10.1021/acs.jctc.3c00651. Epub 2023 Sep 13.
Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.
相对熵最小化是一种用于寻找能产生目标结构系综的势能函数的统计力学方法，已被证明是纳米粒子自组装逆向设计的有力策略。对于给定的目标结构，通过进行模拟来计算相对熵相对于势能函数可调参数的梯度，然后使用基于梯度的迭代优化来更新这些参数。为了数值稳定性，每次迭代可能需要进行小的参数更新和多次迭代，但这会带来相当大的计算开销，因为每次迭代都必须进行新的模拟以重新评估梯度。在这里，我们研究使用代理模型将最小化相对熵的过程与确定其梯度的计算要求较高的过程解耦。我们使用Smolyak稀疏网格上的切比雪夫多项式插值来近似相对熵梯度。我们的方法可能会提高使用相对熵进行逆向设计的稳健性和计算效率，主要适用于具有少量可调参数的物理信息势能函数。
