mlsanityData to 7 Oct 2026

Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

arXiv 2402.12360 ↗First posted 19 Feb 2024math.NA cs.AI cs.NAcited by 8

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Abstract (arXiv)

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a nonlinear state transformation map by solving a system of inhomogeneous functional equations. The performance of the proposed PINN approach is assessed via two illustrative case studies for which the observer linearizing transformation map can be derived analytically. We also perform an uncertainty quantification analysis for the proposed PINN scheme and we compare it with conventional power-series numerical implementations, which rely on the computation of a power series solution.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 17 of its 73 references that are in the map. First posted on arXiv 19 Feb 2024.

Builds on

17 of 73 references.

References · 17

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  4. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  5. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  6. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29
  7. 2022Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEscited by 19
  8. 2022Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation datacited by 18
  9. 2022Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approachcited by 15
  10. 2022A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networkscited by 14
  11. 2023Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learningcited by 10
  12. 2021Deep KKL: Data-driven Output Prediction for Non-Linear Systemscited by 9
5 more
  1. 2022Learning Robust State Observers using Neural ODEs (longer version)cited by 6
  2. 2018Using learning to control artificial avatars in human motor coordination taskscited by 5
  3. 2020Luenberger observers for discrete-time nonlinear systemscited by 5
  4. 2023Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learningcited by 4
  5. 2021Functional observers with linear error dynamics for discrete-time nonlinear systems, with application to fault diagnosiscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 1.

8 papers.

  1. 2024RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operatorscited by 16
  2. 2025LoopTool: Closing the Data-Training Loop for Robust LLM Tool Callscited by 16
  3. 2025Behavior Injection: Preparing Language Models for Reinforcement Learningcited by 8
  4. 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilationcited by 7
  5. 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiologycited by 3
  6. 2025PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systemscited by 1
  7. 2025Designing Robust Software Sensors for Nonlinear Systems via Neural Networks and Adaptive Sliding Mode Controlcited by 0
  8. 2026Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approachcited by 0