Neural Network Approach to Construction of Classical Integrable Systems
| Autor: | Hidemaro Suwa, Fumihiro Ishikawa, Synge Todo |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Artificial neural network Integrable system Nonlinear Sciences - Exactly Solvable and Integrable Systems Computer science FOS: Physical sciences General Physics and Astronomy Computational Physics (physics.comp-ph) Machine Learning (cs.LG) Algebra Nonlinear Sciences::Exactly Solvable and Integrable Systems Physical phenomena Lax pair Exactly Solvable and Integrable Systems (nlin.SI) Physics - Computational Physics |
| Popis: | Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved quantities. Machine learning techniques have recently been applied to broad physics fields and proven powerful for building non-trivial transformations and potential functions. We here propose a machine learning approach to a systematic construction of classical integrable systems. Given the Hamiltonian or samples in latent space, our neural network simultaneously learns the corresponding natural Hamiltonian in real space and the canonical transformation between the latent space and the real space variables. We also propose a loss function for building integrable systems and demonstrate successful unsupervised learning for the Toda lattice. Our approach enables exploring new integrable systems without any prior knowledge about the canonical transformation or any ansatz for the Lax pair. |
| Databáze: | OpenAIRE |
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