Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems

arXiv:2509.20191 · physics.comp-ph, cs.LG, cs.NA, math.NA · Submitted 2025-09-24 · Read on arXiv

physics.comp-ph, cs.LG, cs.NA, math.NA

Submitted: 2025-09-24

Updated: 2026-08-28

Code: https://github.com/aleksjek9/pinnrobustness

Terminology

• Inverse Problem — 27× in this paper · explained in 2 episodes
• Finite Element Method — 12× in this paper
• Accuracy — 8× in this paper · explained in 1 episode
• Adam — 6× in this paper · explained in 2 episodes
• Loss Function — 4× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 3× in this paper · explained in 6 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Sequential Quadratic Programming — 2× in this paper
• Activation Function — 1× in this paper · explained in 1 episode
• Adaptive Weighting — 1× in this paper · explained in 1 episode
• Adjoint Method — 1× in this paper · explained in 1 episode
• Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
• Frustration — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reward Hacking — 1× in this paper · explained in 8 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next
• Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
• Can Physics-Informed Neural Networks beat the Finite Element Method?
• Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration
• Inversion of DC Resistivity Data using Physics-Informed Neural Networks
• A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)
• Identification of Physical Properties in Acoustic Tubes Using Physics-Informed Neural Networks
• Inverse Physics-Informed Neural Networks for transport models in porous materials
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• Adam: A Method for Stochastic Optimization
• Optimizing the optimizer for data driven deep neural networks and physics informed neural networks
• CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics
• Respecting causality is all you need for training physics-informed neural networks
• PyTorch: An Imperative Style, High-Performance Deep Learning Library

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