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About this paper
Lexiang Hu, Yikang Li, Zhouchen Lin
A new method, LieNLSD, discovers the number and explicit mathematical expressions of nonlinear symmetries from dynamic data governed by differential equations. It accurately identified symmetries in various physical systems and enhanced the long-rollout accuracy of neural PDE solvers by over 20%.
Key insights
- The infinitesimal criterion for Lie point symmetries can be expressed as a linear system solvable with respect to the generator's coefficients, even for nonlinear symmetries.
- Parameterizing infinitesimal generators with a flexible function library enables the discovery of diverse linear and nonlinear symmetry types.
- Combining Singular Value Decomposition (SVD) with the LADMAP algorithm yields both the precise dimension of the Lie algebra and interpretable, sparse explicit expressions for the generators.
Summary by alphaXiv.
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