2021/03/31 by Fumihiro Ishikawa, Hidemaro Suwa, Synge Todo
Computer Science · Materials Science · Physics and Astronomy · #Ansatz #Artificial neural network #Canonical transformation #Hamiltonian (control theory) #Hamiltonian system #Integrable system #Lax pair #Machine Learning in Materials Science #Quantum many-body systems #Space (punctuation) #Topological Materials and Phenomena #Transformation (genetics) #cs.LG #nlin.SI #physics.comp-ph
paper · pdf · doi:10.7566/jpsj.90.093001
published as J. Phys. Soc. Jpn. 90, 093001 (2021)
openalex created_date 2021/03/15 · arxiv created 2021/08/30 · openalex publication_date 2021/08/30 · arxiv updated 2021/08/31 · openalex updated_date 2026/08/05
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.