OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration

arXiv:2405.04484v1 Announce Type: new
Abstract: Integrable partial differential equation (PDE) systems are of great interest in natural science, but are exceedingly rare and difficult to discover. To solve this, we introduce OptPDE, a first-of-its-kind machine learning approach that Optimizes PDEs' coefficients to maximize their number of conserved quantities, $n_{\rm CQ}$, and thus discover new integrable systems. We discover four families of integrable PDEs, one of which was previously known, and three of which have at least one conserved quantity but …

abstract arxiv collaboration cs.lg differential differential equation equation human kind machine machine learning natural novel physics.comp-ph science solve systems type via