CLAIMED: A CLAssification-Incorporated Minimum Energy Design to Explore a Multivariate Response Surface With Feasibility Constraints

Abstract

Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations that generate output close to some desired or “target” vector. Despite reducing the problem to exploration of the input space with respect to a 1-D loss function, the search is nontrivial and challenging due to infeasible input combinations, high dimensionalities of the input and output space and multiple “desirable” regions in the input space, and the difficulty of emulating the objective function well with a surrogate model. We propose an approach that is based on combining machine learning techniques with smart experimental design ideas to locate multiple good regions in the input space. Note to Practitioners—ReaxFF is a force field that incorporates complex functions with associated inputs in order to describe the inter- and intra-atomic interactions in materials systems. A typical ReaxFF force field consists of hundreds of parameters (inputs) per element type. During the development of a force field for a molecular system of interest, using computer simulations, these parameters are optimized to reproduce hundreds of material properties close to some benchmark reference values. Finding “good” combinations of hundreds of parameters that produce hundreds of reference values close to their gold standards is a challenging problem because there may be several parameter combinations that may be “almost equally good” or “equally desirable.” To add to the complication, several input combinations simply lead to a system crash, not producing any output at all. Standard global optimization methods do not address such a problem. We propose a novel framework that can address this problem. Beyond the ReaxFF optimization, it can be applied to multiobjective optimization in engineering and the physical sciences, where there are unknown constraints and the focus is on obtaining several good points that can serve as alternatives to a single global optimum.