Discovering Governing Physics in the Presence of Uncertainty

In the study of complex dynamical systems, accurately modeling the underlying physics is crucial for predicting system behavior. Yet real-world systems exhibit pronounced input variability and are observed through noisy, limited data that confound traditional methods assuming fixed-coefficient models. In this work, we theorize that accounting for system variability together with measurement noise is the key to consistently discover the governing equations underlying dynamical systems. We introduce a stochastic inverse physics-discovery (SIP) framework that treats unknown coefficients as random variables and infers their posterior distributions by minimizing the Kullback-Leibler divergence between the push-forward of posterior samples and the empirical data distribution. Tests on ten scenarios spanning predator-prey dynamics, chaotic attractors, oscillatory systems, ecological records, and liquid infiltration demonstrate that SIP consistently outperforms seven methods across three paradigms, reducing coefficient error by about 80% and achieving perfect structural identification in seven of ten cases.