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Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation

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arxiv 2410.05445 v1 pith:6QSAQBD7 submitted 2024-10-07 nlin.PS cs.LG

Shaoxuan Chen , Panayotis G. Kevrekidis , Hong-Kun Zhang , Wei Zhu This is my paper · ORCID
classification nlin.PScs.LG
keywords methodsystemconservationlawsdeflationlatticeneuraltowards
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In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi-Pasta-Ulam-Tsingou lattice and the Calogero-Moser system.

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  1. On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

    cs.LG 2026-07 accept novelty 5.5 of 10

    The first broad taxonomy of post-hoc PDE-discovery metrics shows single scores mislead, and recommends multi-criteria evaluation with OOD and physics checks.

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