# Two-Dimensional Wave Equation Benchmark

Continuous symmetries are usually found by writing the differential equations symbolically and solving an overdetermined determining system; here the search runs directly on sampled jet data through a linear operator that separates admissible generators from redundant directions. On a two-dimensional wave-equation benchmark the procedure recovers eleven generators in sequence, keeps validation symmetry residuals near machine precision, and reproduces Lie-bracket closure in a post-recovery check.

Continuous symmetries are usually found by writing the differential equations symbolically and solving an overdetermined determining system; here the search runs directly on sampled jet data through a linear operator that separates admissible generators from redundant directions. On a two-dimensional wave-equation benchmark the procedure recovers eleven generators in sequence, keeps validation symmetry residuals near machine precision, and reproduces Lie-bracket closure in a post-recovery check.