mlsanityData to 7 Oct 2026

Physics-informed neural networks for solving parametric magnetostatic problems

arXiv 2202.04041 ↗First posted 8 Feb 2022cs.CE cs.LG physics.comp-phcited by 10

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Abstract (arXiv)

The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. First, we present a functional whose minimization is equivalent to solving parametric magnetostatic problems. Subsequently, we use a deep neural network (DNN) to represent the magnetic field as a function of space and parameters that describe geometric features and operating points. We train the DNN by minimizing the physics-informed functional using stochastic gradient descent. Lastly, we demonstrate our approach on a mboxten-dimensional EI-core electromagnet problem with parameterized geometry. We evaluate the accuracy of the DNN by comparing its predictions to those of finite element analysis.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 26 of its 135 references that are in the map. First posted on arXiv 8 Feb 2022.

Builds on

26 of 135 references.

References · 26

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2018On the Spectral Bias of Neural Networkscited by 1,321
  5. 2015Automatic differentiation in machine learning: a surveycited by 846
  6. 2014Deep Learning in Neural Networks: An Overviewcited by 765
  7. 2016TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systemscited by 660
  8. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  9. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  10. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  11. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  12. 2020Universal Differential Equations for Scientific Machine Learningcited by 345
14 more
  1. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  2. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  3. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  4. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  5. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 127
  6. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
  7. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  8. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
  9. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  10. 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
  11. 2020Physics-informed neural network for ultrasound nondestructive quantification of surface breaking crackscited by 67
  12. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
  13. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  14. 2019PyDEns: a Python Framework for Solving Differential Equations with Neural Networkscited by 14

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Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 3; 2025: 4.

10 papers.

  1. 2023Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networkscited by 17
  2. 2024Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methodscited by 10
  3. 2023Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantificationcited by 9
  4. 2024Physics-informed Discretization-independent Deep Compositional Operator Networkcited by 6
  5. 2022Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Datacited by 4
  6. 2024Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networkscited by 2
  7. 2025Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networkscited by 2
  8. 2025Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Weldingcited by 0
  9. 2025Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domainscited by 0
  10. 2025Intelligent Optimization of Multi-Parameter Micromixers Using a Scientific Machine Learning Frameworkcited by 0