mlsanityData to 14 Oct 2026

A comprehensive analysis of PINNs: Variants, Applications, and Challenges

arXiv 2505.22761 ↗First posted 28 May 2025cs.CE cs.AIcited by 1

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Abstract (arXiv)

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 23 of its 68 references that are in the map. First posted on arXiv 28 May 2025.

Builds on

23 of 68 references.

References · 23

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  3. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 123
  4. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 98
  5. 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 76
  6. 2019Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networkscited by 64
  7. 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 44
  8. 2021HyperPINN: Learning parameterized differential equations with physics-informed hypernetworkscited by 39
  9. 2021Physics-informed neural networks for the shallow-water equations on the spherecited by 32
  10. 2020PIGNet: A physics-informed deep learning model toward generalized drug-target interaction predictionscited by 31
  11. 2021DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networkscited by 28
  12. 2020Solving inverse-PDE problems with physics-aware neural networkscited by 27
11 more
  1. 2020Training Generative Adversarial Networks by Solving Ordinary Differential Equationscited by 21
  2. 2021Composing Partial Differential Equations with Physics-Aware Neural Networkscited by 21
  3. 2021Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equationscited by 13
  4. 2021Interval and fuzzy physics-informed neural networks for uncertain fieldscited by 9
  5. 2022Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problemscited by 9
  6. 2022Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equationscited by 7
  7. 2022A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiencycited by 7
  8. 2022Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Supportcited by 6
  9. 2023Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark testscited by 4
  10. 2022High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networkscited by 2
  11. 2023Physics-informed Neural Network: The Effect of Reparameterization in Solving Differential Equationscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026QGPINNs: A Physics-Informed Neural Network Framework for Nonlocal Differential Equations on Quantum Graphscited by 0