From Flow-Box Invariants to Global Conservation Laws: Machine Learning-Assisted Detection of Singularities and Near-Integrability

Conservation laws reveal invariant structure in dynamical systems and constrain their evolution to lower-dimensional level sets. Locally, however, per the flow-box theorem, every $d$-dimensional system generically admits $d-1$ functionally independent conservation laws near a regular point even though, generically, only a few such laws persist globally. Data-driven methods typically learn conservation laws on a prescribed region of phase space from which training samples are drawn, leaving their behavior beyond that region unresolved. We formulate this local-to-global continuation problem and…

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