Orders-of-coupling representation with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization
This is an incremental improvement for applications in quantum dynamics and other fields requiring integration, offering a more convenient method for constructing low-dimensional function representations.
The paper tackles the problem of building orders-of-coupling representations for multivariate functions, such as molecular potential energy surfaces, by proposing a neural network model that uses optimal neuron activation functions computed with a first-order additive Gaussian process regression and avoids nonlinear parameter optimization.
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.