Year: 2026
Type: preprint
Abstract: We consider the problem of PDE discovery from possibly noisy observations under the hypothesis that the underlying dynamic is symmetric in all rigid motions. Rather than using a generic library of derivative monomials, we leverage this assumption to construct libraries whose candidate terms are themselves rigid-motion-equivariant, and combine them with sparse regression to benchmark such libraries over five different equations. The advantage is most pronounced when the noise itself breaks rigid-motion symmetry (e.g., radially or axially varying noise), and when the ambient spatial dimension increases, in which case they are also less resource intensive.
Source: arXiv (Cornell University)
Authors: Ballerin, Francesco, Grong, Erlend
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202213423
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