mlsanityData to 7 Oct 2026

Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks

arXiv 2005.03596 ↗First posted 7 May 2020cs.LG stat.MLcited by 67

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Abstract (arXiv)

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 May 2020.

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Citing papers per year: 2021: 9; 2022: 15; 2023: 12; 2024: 18; 2025: 7; 2026: 6.

67 papers.

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  1. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  2. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  3. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
  4. 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
  5. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  6. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  7. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  8. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  9. 2021Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functionscited by 49
  10. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  11. 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
  12. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
38 more
  1. 2022PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solverscited by 22
  2. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  3. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  4. 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
  5. 2024VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behaviorcited by 13
  6. 2022Physics-informed neural networks for solving parametric magnetostatic problemscited by 10
  7. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  8. 2022Spiking Neural Operators for Scientific Machine Learningcited by 8
  9. 2024Speeding up and reducing memory usage for scientific machine learning via mixed precisioncited by 8
  10. 2022A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiencycited by 7
  11. 2022Semi-analytic PINN methods for singularly perturbed boundary value problemscited by 6
  12. 2024NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elementscited by 6
  13. 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
  14. 2026Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelinescited by 6
  15. 2022Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networkscited by 5
  16. 2022Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networkscited by 5
  17. 2024Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equationscited by 5
  18. 2024Robust Weight Initialization for Tanh Neural Networks with Fixed Point Analysiscited by 5
  19. 2025Neural Variable-Order Fractional Differential Equation Networkscited by 5
  20. 2023Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNscited by 4
  21. 2025Position: Biology is the Challenge Physics-Informed ML Needs to Evolvecited by 4
  22. 2021PINNs for the Solution of the Hyperbolic Buckley-Leverett Problem with a Non-convex Flux Functioncited by 3
  23. 2022Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEscited by 3
  24. 2024Physics and geometry informed neural operator network with application to acoustic scatteringcited by 3
  25. 2025iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filtercited by 3
  26. 2026Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensemblescited by 3
  27. 2023Reconstructing Rayleigh-Benard flows out of temperature-only measurements using Physics-Informed Neural Networkscited by 2
  28. 2024Real-Time 2D Temperature Field Prediction in Metal Additive Manufacturing Using Physics-Informed Neural Networkscited by 2
  29. 2026Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regimecited by 2
  30. 2021Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networkscited by 1
  31. 2021Wave-Informed Matrix Factorization with Global Optimality Guaranteescited by 1
  32. 2022Utilising physics-guided deep learning to overcome data scarcitycited by 1
  33. 2023An information field theory approach to Bayesian state and parameter estimation in dynamical systemscited by 1
  34. 2023Training Physics-Informed Neural Networks via Multi-Task Optimization for Traffic Density Predictioncited by 1
  35. 2023On Training Derivative-Constrained Neural Networkscited by 1
  36. 2023Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning frameworkcited by 1
  37. 2024Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networkscited by 1
  38. 2024Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metricscited by 1

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