Physics-Informed Machine Learning for Characterizing System Stability

• URL: http://arxiv.org/abs/2511.08831v1
• Date: Thu, 13 Nov 2025 01:10:32 GMT
• Title: Physics-Informed Machine Learning for Characterizing System Stability
• Abstract summary: A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive.<n>Existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations.<n>We present a new physics-informed machine learning method of characterizing an estimated stability region.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

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