mlsanityData to 7 Oct 2026

Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks

arXiv 2210.10646 ↗First posted 19 Oct 2022cs.LG cs.NA math.NAcited by 4

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Abstract (arXiv)

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly corrupted due to the possible sensor mechanism failing. We propose the Least Absolute Deviation based PINN (LAD-PINN) to reconstruct the solution and recover unknown parameters in PDEs - even if spurious data or outliers corrupt a large percentage of the observations. To further improve the accuracy of recovering hidden physics, the two-stage Median Absolute Deviation based PINN (MAD-PINN) is proposed, where LAD-PINN is employed as an outlier detector followed by MAD screening out the highly corrupted data. Then the vanilla PINN or its variants can be subsequently applied to exploit the remaining normal data. Through several examples, including Poisson's equation, wave equation, and steady or unsteady Navier-Stokes equations, we illustrate the generalizability, accuracy and efficiency of the proposed algorithms for recovering governing equations from noisy and highly corrupted measurement data.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 21 of its 47 references that are in the map. First posted on arXiv 19 Oct 2022.

Builds on

21 of 47 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  4. 2017Certified Defenses for Data Poisoning Attackscited by 288
  5. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  6. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  7. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  8. 2019Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networkscited by 162
  9. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  10. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
  11. 2019PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEscited by 116
  12. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
9 more
  1. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
  2. 2020A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecturecited by 50
  3. 2021Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusioncited by 38
  4. 2021SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEscited by 32
  5. 2022Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?cited by 23
  6. 2022RANG: A Residual-based Adaptive Node Generation Method for Physics-Informed Neural Networkscited by 14
  7. 2022State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learningcited by 12
  8. 2021IDRLnet: A Physics-Informed Neural Network Librarycited by 10
  9. 2014Robust Linear Regression: A Review and Comparisoncited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 2.

4 papers.

  1. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  2. 2024A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detectioncited by 2
  3. 2026naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurementcited by 1
  4. 2024SGD Jittering: A Training Strategy for Robust and Accurate Model-Based Architecturescited by 0