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LieDiscover introduces a reinforcement learning-enhanced encoder-decoder framework that dynamically expands symbolic libraries to uncover complex symmetries in scientific data. By optimizing the function library alongside coefficients, this method overcomes limitations of static approaches when dealing with high-order polynomials or transcendental functions. The resulting open-form infinitesimal generators significantly improve performance in downstream partial differential equation solving and discovery tasks.
LieDiscover: Adaptive Symbolic Library Construction for Explicit Open-form Symmetry Discovery
arXiv:2609.33663v1 Announce Type: cross Abstract: Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.
Abstract:Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.
Symbolic Computation (cs.SC); Machine Learning (cs.LG)
arXiv:2609.33663 [cs.SC]
(or arXiv:2609.33663v1 [cs.SC] for this version)
https://doi.org/10.48550/arXiv.2609.33663 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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