Intrinsic Lie point symmetries discovered from differential equation data
Original title: Data-driven discovery of intrinsic Lie point symmetries of differential equation systems
Framework identifies complete generator sets and reproduces Lie-bracket structure from sampled jet-space data.
The method formulates intrinsic Lie point-symmetry discovery as an operator-theoretic problem on sampled jet-space data. Admissible generators are identified from a sampled determining operator and separated from redundant directions. On a benchmark with an 11-dimensional represented intrinsic symmetry algebra, the approach recovers the full generator set, reproduces its Lie-bracket structure to numerical precision, and approximates a known generator beyond the training domain.
- Recovers complete represented generator set on 11-dimensional algebra
- Reproduces Lie-bracket structure to numerical precision
- Approximates known generator beyond training domain
- Uses prolongation, sequential subspace restrictions and nonlinear dictionary
- Rank-stabilization preflight test diagnoses non-stabilizing systems
From the original article
1 min read at arxiv.orgDiscovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations or a closed-form representation of the governing system. We formulate intrinsic Lie point-symmetry discovery as an operator-theoretic problem on sampled jet-space data.
By Ilker Gurcan · arxiv.org
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