Published: Nov 14, 2025 by Daning Huang
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity and reveal hidden physics. However, identifying Lie symmetries directly from scattered data, without explicit knowledge of the governing equations, remains a significant challenge. Our work introduces a novel numerical scheme that can recover continuous symmetries (e.g., rotations) without requiring the analytical form of the differential equations. Furthermore, the scheme is grounded by the theory of manifold learning and provably convergent.
The possible applications of the method are vast: from Hamiltonian dynamics in space to fluid and solid dynamics, or anything involving complex differential equations (ordinary, partial, with algebraic constraints, with intergals, etc.). We are open to any potential collaborations in applying the algorithms. The first version of the code is available here.
This work is supported by NSF CDSE Program.
