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

TL;DR

This paper introduces an extended neural deflation method that identifies conservation laws directly from system trajectories, enabling data-driven discovery of invariants in complex dynamical systems without explicit equations.

Contribution

It advances previous work by developing a trajectory-based approach for conservation law discovery, broadening applicability to systems with only observational data.

Findings

Successfully identified conservation laws in harmonic oscillators

Applied to complex systems like Toda lattice and Calogero-Moser

Demonstrated effectiveness with discrete trajectory data

Abstract

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.