{"paper":{"title":"AI Poincar\\'{e} 2.0: Machine Learning Conservation Laws from Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.EP","nlin.SI","physics.class-ph","physics.flu-dyn"],"primary_cat":"cs.LG","authors_text":"Max Tegmark (MIT), Varun Madhavan (IIT), Ziming Liu (MIT)","submitted_at":"2022-03-23T17:57:01Z","abstract_excerpt":"We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schr\\\"odinger equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12610","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.12610/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}