Neural network matrix product operator: A multi-dimensionally integrable machine learning potential

A neural network-based machine learning potential energy surface (PES) expressed in a matrix product operator (NN-MPO) is proposed. The MPO form enables efficient evaluation of high-dimensional integrals that arise in solving the time-dependent and time-independent Schrödinger equation, and effectiv...

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Bibliographic Details
Main Authors: Kentaro Hino, Yuki Kurashige
Format: Article
Language:English
Published: American Physical Society 2025-06-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.7.023217
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Summary:A neural network-based machine learning potential energy surface (PES) expressed in a matrix product operator (NN-MPO) is proposed. The MPO form enables efficient evaluation of high-dimensional integrals that arise in solving the time-dependent and time-independent Schrödinger equation, and effectively overcomes the so-called curse of dimensionality. This starkly contrasts with other neural network-based machine learning PES methods, such as multilayer perceptrons (MLPs), where evaluating high-dimensional integrals is not straightforward due to the fully connected topology in their backbone architecture. Nevertheless, the NN-MPO retains the high representational capacity of neural networks. NN-MPO can achieve spectroscopic accuracy with a test mean absolute error (MAE) of 3.03 cm^{−1} for a fully coupled six-dimensional ab initio PES, using only 625 training points distributed across a 0 to 17 000 cm^{−1} energy range.
ISSN:2643-1564