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<p>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.</p>

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Discovering Governing Physics in the Presence of Uncertainty

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月25日

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  • Ridwan Olabiyi,
  • Han Hu,
  • Ashif Iquebal

摘要

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.