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OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration
May 8, 2024, 4:42 a.m. | Subhash Kantamneni, Ziming Liu, Max Tegmark
cs.LG updates on arXiv.org arxiv.org
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 …
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