(272j) Surrogate Modeling of the Relative Entropy for Inverse Design

Relative entropy minimization—a statistical-mechanics approach for finding molecular interactions that produce target structural ensembles—is a powerful approach for inverse design of soft materials. For a given set of parameters describing a molecular interaction, the gradient of the relative entropy is evaluated by performing a molecular simulation, then the parameters are updated using gradient-descent methods. Small descent steps are often needed for numerical stability, incurring considerable computational expense because a simulation must be performed at each step. Gradient-descent methods may also fail to find the true optimum (global minimum of the relative entropy) because they can converge to suboptimal local minima depending on the initial value of the parameters. Here, we investigate the use of surrogate modeling to reconstruct the relative entropy from sparse sampling of its gradient. We approximate the relative entropy with Chebyshev polynomial interpolation on Smolyak sparse grids, giving a function that is inexpensive to evaluate and is amenable to standard optimization techniques. We then identify approximate locations of minima in the relative entropy that we can use as starting points for standard relative-entropy minimization using gradient descent. By identifying these good initial values, our work increases the robustness and computational efficiency of the relative-entropy minimization protocol.