2023/03/28 by Wei Zhu, Zhu, Wei, Hong-Kun Zhang +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Materials Science · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Conservation law #Conserved quantity #Deflation #Dynamical systems theory #Economics #FOS: Physical sciences #Hamiltonian (control theory) #Integrable system #Machine Learning in Materials Science #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Model Reduction and Neural Networks #Pattern Formation and Solitons (nlin.PS) #Physics #Protein Structure and Dynamics #Quantum mechanics
paper · pdf · doi:10.48550/arxiv.2303.15958
openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to iteratively train a number of neural networks to minimize a regularized loss function accounting for the necessity of conserved quantities to be \it in involution and enforcing functional independence thereof consistently in the infinite-sample limit. The method is applied to a series of integrable and non-integrable lattice differential-difference equations. In the former, the predicted number of conservation laws extensively grows with the number of degrees of freedom, while for the latter, it generically stops at a threshold related to the number of conserved quantities in the system. This data-driven tool could prove valuable in assessing a model's conserved quantities and its potential integrability.