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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-06-01
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| 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. |
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| ISSN: | 2643-1564 |