Automated structural learning of stochastic dynamics

Xeniya Bashkova, Alexander Hvatov

Keywords: equation discovery, stochastic differential equations, structural learning

Abstract: While automated equation discovery has successfully extracted deterministic models from time-series data, extending these methods to stochastic systems remains a critical problem. Existing symbolic regression tools typically yield rigid Ordinary Differential Equations (ODEs) or disjointed ensembles, failing to capture intrinsic system uncertainty without sacrificing analytical interpretability. To resolve this, we introduce a framework that recasts equation discovery as a probabilistic inference task. This approach harnesses the inherent stochasticity of evolutionary optimization, mapping the structural variability across multiple symbolic regression executions into continuous probability distributions over mathematical terms and coefficients. This mechanism bypasses restrictive parametric assumptions, directly distilling noisy observations into a single, cohesive Stochastic Differential Equation (SDE). Unlike opaque neural architectures or unwieldy ODE ensembles, our framework generates compact, transparent models that are natively equipped for formal symbolic manipulation and rigorous mathematical reasoning.

Submission Number: 47