PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems

2025/07/09 by Farkane, Ayoub, Boutayeb, Mohamed, Oudani, Mustapha +1
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2507.06712

Abstract

State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability.

Citations

• Unsupervised Physics-Informed Neural Network-based Nonlinear Observer design for autonomous systems using contraction analysis
• Physics-Informed Neural Networks for Accelerating Power System State Estimation
• Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems
• Towards gain tuning for numerical KKL observers
• Multi-Objective Loss Balancing for Physics-Informed Deep Learning
• Multi-fidelity Bayesian neural networks: Algorithms and applications
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Neural Ordinary Differential Equations
• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

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