analiza aiqbench
LieStoNet advances the intersection of machine learning and mathematical physics by enabling neural networks to discover continuous Lie symmetries in stochastic dynamical systems without predefined templates. This template-free approach improves sample efficiency and robustness for modeling noisy dynamics, directly addressing a gap where symmetry principles are typically unknown or inaccessible in complex SDEs. By enforcing strict adherence to Lie algebra axioms during training, the framework provides interpretable generators that align with ground-truth symmetry algebras across canonical benchmarks.
LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems
arXiv:2608.01582v1 Announce Type: cross Abstract: Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \textit{LieStoNet}, an end-to-end, \emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{https://github.com/sumit-sinha-seas/LieStoNet_Final.git}{this link}.
Abstract:Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \textit{LieStoNet}, an end-to-end, \emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{this https URL}{this link}.
25 Pages, 7 figures. Accepted to the International Conference on Machine Learning (ICML 2026)
Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Mathematical Physics (math-ph)
arXiv:2608.01582 [cond-mat.stat-mech]
(or arXiv:2608.01582v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2608.01582 arXiv-issued DOI via DataCite (pending registration)
Text integral sub licența deschisă a publicației · 228 cuvinte
Subiecte conexe
Local error correction prolongs time-crystalline memory
arXiv · 14 oct. 2026
Koopman Theory and Metaethics
LessWrong · 19 sept. 2026
Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds
arXiv · 17 sept. 2026
Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials
arXiv · 5 iun. 2026