  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.
