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Nonlinear discrete-time observers with Physics-Informed Neural Networks

Author

Listed:
  • Vargas Alvarez, Hector
  • Fabiani, Gianluca
  • Kazantzis, Nikolaos
  • Kevrekidis, Ioannis G.
  • Siettos, Constantinos

Abstract

We use physics-informed neural networks (PINNs) to numerically solve the discrete-time nonlinear observer-based state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation operator by solving a system of functional equations. The performance of the proposed approach is assessed via two illustrative case studies, for which the observer linearizing transformation operator can be derived analytically. We also perform an uncertainty quantification analysis for the proposed scheme. The performance and numerical approximation accuracy of the proposed scheme is compared with conventional power-series numerical implementation.

Suggested Citation

  • Vargas Alvarez, Hector & Fabiani, Gianluca & Kazantzis, Nikolaos & Kevrekidis, Ioannis G. & Siettos, Constantinos, 2024. "Nonlinear discrete-time observers with Physics-Informed Neural Networks," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007677
    DOI: 10.1016/j.chaos.2024.115215
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    References listed on IDEAS

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    1. Gianluca Fabiani & Nikolaos Evangelou & Tianqi Cui & Juan M. Bello-Rivas & Cristina P. Martin-Linares & Constantinos Siettos & Ioannis G. Kevrekidis, 2024. "Task-oriented machine learning surrogates for tipping points of agent-based models," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    2. Enrico Schiassi & Mario De Florio & Andrea D’Ambrosio & Daniele Mortari & Roberto Furfaro, 2021. "Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models," Mathematics, MDPI, vol. 9(17), pages 1-17, August.
    3. Bethany Lusch & J. Nathan Kutz & Steven L. Brunton, 2018. "Deep learning for universal linear embeddings of nonlinear dynamics," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
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