(248d) Approximating Anisotropic Pairwise Potential Energy Surfaces Using Mixed Basis Surrogate Models with Sparse Sampling

Accurately approximating anisotropic interactions poses a significant mathematical and computational challenge because these interactions depend on up to six configurational degrees of freedom. Surrogate models trained on limited data sampled on a predefined sparse grid in configuration space are a promising strategy to address this challenge. Here, we design surrogate models for anisotropic pairwise interactions using mixed basis interpolants on Smolyak sparse grids. We first apply a physics-informed coordinate transformation that significantly improves approximation accuracy. This transformation naturally identifies aperiodic and periodic configuration coordinates, which we represent using a basis of Chebyshev polynomials and trigonometric functions, respectively. We test our approach for different physical problems, including the interactions between dipoles and between shape-anisotropic nanoparticles. We also compare our strategy to state-of-the-art machine-learning alternatives and compare accuracies as a function of amount of sampled data. We anticipate that our approach will be generally useful for approximating anisotropic potentials of mean force and torque for mesoscale simulations.