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

arXiv: https://arxiv.org/abs/2302.12013 · HTML: https://mlsanity.com/paper/2302.12013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 82 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 3 of 3)

- [On the optimization of hyperparameters in Gaussian process regression with the help of low-order high-dimensional model representation](https://mlsanity.com/paper/2112.01374/) (2021)
- [Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method](https://mlsanity.com/paper/2012.02704/) (2020)
- [Neural network with optimal neuron activation functions based on additive Gaussian process regression](https://mlsanity.com/paper/2301.05567/) (2023)

## Built on by (most cited first, 1 of 1)

- [Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension](https://mlsanity.com/paper/2311.10790/) (2023)

## Abstract (arXiv)

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.