تقرير
Machine learning independent conservation laws through neural deflation
| العنوان: | Machine learning independent conservation laws through neural deflation |
|---|---|
| المؤلفون: | Zhu, Wei, Zhang, Hong-Kun, Kevrekidis, P. G. |
| سنة النشر: | 2023 |
| المجموعة: | Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Pattern Formation and Solitons |
| الوصف: | 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. Comment: 6 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.15958 |
| رقم الأكسشن: | edsarx.2303.15958 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |