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

Orders-of-coupling representations (representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates corresponding to different orders of coupling) are useful in many applications, for example, in computational chemistry and other applications, especially where integration is needed. Examples include N-mode approximations and many-body expansions. 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. Commun. 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.