Neural Network Matrix Product Operator: A Multi-Dimensionally Integrable Machine Learning Potential
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915274675978240 |
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| author | Hino, Kentaro Kurashige, Yuki |
| author_facet | Hino, Kentaro Kurashige, Yuki |
| contents | 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 multi-layer 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. Our Python implementation is available at https://github.com/KenHino/Pompon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23858 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Network Matrix Product Operator: A Multi-Dimensionally Integrable Machine Learning Potential Hino, Kentaro Kurashige, Yuki Machine Learning Disordered Systems and Neural Networks Statistical Mechanics Chemical Physics Quantum Physics 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 multi-layer 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. Our Python implementation is available at https://github.com/KenHino/Pompon. |
| title | Neural Network Matrix Product Operator: A Multi-Dimensionally Integrable Machine Learning Potential |
| topic | Machine Learning Disordered Systems and Neural Networks Statistical Mechanics Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2410.23858 |