mlsanityData to 7 Oct 2026

Conditional physics informed neural networks

arXiv 2104.02741 ↗First posted 6 Apr 2021cs.LG cond-mat.mtrl-scicited by 23

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Abstract (arXiv)

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local defects. When the neural network incorporates the physics of magnetization reversal, training can be achieved in an unsupervised way. There is no need to generate labeled training data. The presented test cases have been rigorously studied in the past. Thus, a detailed and easy comparison with analytical solutions is made. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 8 of its 45 references that are in the map. First posted on arXiv 6 Apr 2021.

Builds on

8 of 45 references.

References · 8

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  4. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 144
  5. 2018Deep Fluids: A Generative Network for Parameterized Fluid Simulationscited by 121
  6. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
  7. 2019PyDEns: a Python Framework for Solving Differential Equations with Neural Networkscited by 14
  8. 2020An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradientcited by 13

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Cited by year

Citing papers per year: 2021: 1; 2022: 7; 2023: 4; 2024: 4; 2025: 7.

23 papers.

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  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  3. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  4. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
  5. 2023Can Physics-Informed Neural Networks beat the Finite Element Method?cited by 68
  6. 2025Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspectivecited by 55
  7. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  8. 2023Machine learning and domain decomposition methods -- a surveycited by 14
  9. 2022State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learningcited by 12
  10. 2025Solving engineering eigenvalue problems with neural networks using the Rayleigh quotientcited by 8
  11. 2022Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Networkcited by 5
  12. 2023Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performancecited by 5
11 more
  1. 2025AI for Scientific Discovery is a Social Problemcited by 3
  2. 2025Enforcing hidden physics in physics-informed neural networkscited by 3
  3. 2022Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissuecited by 2
  4. 2024Towards Automated Knowledge Integration From Human-Interpretable Representationscited by 2
  5. 2021Predicting the spread of COVID-19 in Delhi, India using Deep Residual Recurrent Neural Networkscited by 1
  6. 2022Application of machine learning regression models to inverse eigenvalue problemscited by 1
  7. 2024PACMANN: Point Adaptive Collocation Method for Artificial Neural Networkscited by 1
  8. 2025Precipitation nowcasting of satellite data using physically-aligned neural networkscited by 1
  9. 2024Physics aware machine learning for micromagnetic energy minimization: recent algorithmic developmentscited by 0
  10. 2025PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Modelscited by 0
  11. 2025Physics-informed low-rank neural operators with application to parametric elliptic PDEscited by 0