Orders-of-coupling representation with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization

TL;DR

This paper introduces a neural network approach with optimal activation functions for representing multivariate functions of different coupling orders, eliminating the need for nonlinear parameter optimization, with applications to molecular potential energy surfaces.

Contribution

The paper presents a novel neural network method using optimal activation functions derived from Gaussian process regression, simplifying the construction of coupling representations without nonlinear optimization.

Findings

Effective representation of molecular potential energy surfaces.

Avoidance of nonlinear parameter optimization in neural network training.

Demonstrated applicability to quantum dynamics and related fields.

Abstract

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where integration is needed. Such representations can be conveniently built with machine learning methods, and previously, methods building the lower-dimensional terms of such representations with neural networks [e.g. Comput. Phys. Comm. 180 (2009) 2002] and Gaussian process regressions [e.g. Mach. Learn. Sci. Technol. 3 (2022) 01LT02] were proposed. Here, we show that neural network models of orders-of-coupling representations can be easily built by using a recently proposed neural network with optimal neuron activation functions computed with a first-order additive Gaussian process regression [arXiv:2301.05567] and avoiding non-linear parameter optimization. Examples are given of representations of molecular potential energy surfaces.