(525d) Surrogate Modelling of Anisotropic Pair Potentials Using Smolyak Sparse Grids

Mathematically representing the effective pairwise interaction between complex anisotropic bodies is challenging because the interaction can depend on many coordinates and the functional form of the interaction is generally unknown. For example, the pairwise potential of mean force and torque (PMFT) between two rigid body proteins can depend on up to 6 coordinates (relative position and orientation vectors) and is computationally demanding to evaluate. Surrogate models can represent such complex functions by sampling them for a set of inputs and training a model to approximate the function over its entire domain. Here, we develop a surrogate modelling approach to approximate anisotropic pair potentials from limited data using Chebyshev polynomial interpolants on Smolyak sparse grids. We test our approach on several model anisotropic potentials and a toy model of the TMV coat protein. With judicious variable transformations and regularization, good approximations of the potentials are obtained. We anticipate this methodology will be used to compute PMFTs from atomistic simulations to enable ultra-coarse-grained simulations of protein solutions at unprecedented length and time scales.