mlsanityData to 7 Oct 2026

Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

arXiv 1907.02531 ↗First posted 4 Jul 2019stat.ML cs.LGcited by 116

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Abstract (arXiv)

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy of the system. Additionally, we modify the neural network output such that the boundary conditions associated with the problem are exactly satisfied. Compared to conventional residual based PINN, the proposed approach has two major advantages. First, the imposition of boundary conditions is relatively simpler and more robust. Second, the order of derivatives present in the functional form of the variational energy is of lower order than in the residual form. Hence, training the network is faster. To compute the total variational energy of the system, an efficient scheme that takes as input a geometry described by spline based CAD model and employs Gauss quadrature rules for numerical integration has been proposed. Moreover, we utilize the concept of transfer learning to obtain the crack path in an efficient manner. The proposed approach is used to solve four fracture mechanics problems. For all the examples, results obtained using the proposed approach match closely with the results available in the literature. For the first two examples, we compare the results obtained using the proposed approach with the conventional residual based neural network results. For both the problems, the proposed approach is found to yield better accuracy compared to conventional residual based PINN algorithms.

Key facts. Cited by 116 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jul 2019.

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Citing papers per year: 2021: 21; 2022: 18; 2023: 30; 2024: 23; 2025: 17; 2026: 7.

116 papers.

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  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  3. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  4. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  5. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  6. 2022Physics-Informed Deep Neural Operator Networkscited by 110
  7. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
  8. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  9. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 98
  10. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  11. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  12. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 86
38 more
  1. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  2. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 77
  3. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  4. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  5. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
  6. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  7. 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
  8. 2021Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural networkcited by 35
  9. 2024A review on data-driven constitutive laws for solidscited by 35
  10. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  11. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 30
  12. 2022Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equationscited by 28
  13. 2023Physics informed WNOcited by 26
  14. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  15. 2023Efficient physics-informed neural networks using hash encodingcited by 21
  16. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  17. 2022Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysmscited by 14
  18. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
  19. 2025Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptationcited by 14
  20. 2025Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemblecited by 13
  21. 2024Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architecturescited by 12
  22. 2021Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodelscited by 10
  23. 2023A foundational neural operator that continuously learns without forgettingcited by 10
  24. 2024A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformationscited by 10
  25. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  26. 2021Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learningscited by 9
  27. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  28. 2023Residual-Based Error Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problemscited by 9
  29. 2023Spectral operator learning for parametric PDEs without data reliancecited by 9
  30. 2024Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learningcited by 9
  31. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  32. 2022WaveY-Net: Physics-augmented deep learning for high-speed electromagnetic simulation and optimizationcited by 8
  33. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  34. 2025Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modelingcited by 8
  35. 2021Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systemscited by 7
  36. 2022Leveraging Industry 4.0 -- Deep Learning, Surrogate Model and Transfer Learning with Uncertainty Quantification Incorporated into Digital Twin for Nuclear Systemcited by 7
  37. 2021GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equationscited by 6
  38. 2021DeepPhysics: a physics aware deep learning framework for real-time simulationcited by 6

50 most cited of 116 All 116 (JSON)