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

arXiv: https://arxiv.org/abs/2507.06712 · HTML: https://mlsanity.com/paper/2507.06712/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Towards gain tuning for numerical KKL observers](https://mlsanity.com/paper/2204.00318/) (2022)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems](https://mlsanity.com/paper/2210.01476/) (2022)
- [Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.12360/) (2024)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
- [Physics-Informed Neural Networks for Satellite State Estimation](https://mlsanity.com/paper/2403.19736/) (2024)
- [Unsupervised Physics-Informed Neural Network-based Nonlinear Observer design for autonomous systems using contraction analysis](https://mlsanity.com/paper/2411.09237/) (2024)
- [Convergence of Nonlinear Observers on R^n with a Riemannian Metric (Part II)](https://mlsanity.com/paper/1606.05834/) (2016)

## Built on by (most cited first, 1 of 1)

- [Mathematical Modeling of Cancer-Bacterial Therapy: Analysis and Numerical Simulation via Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.19326/) (2026)

## Abstract (arXiv)

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.