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

arXiv: https://arxiv.org/abs/2505.22761 · HTML: https://mlsanity.com/paper/2505.22761/

## Key facts

- Cited by 1 papers 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 (most cited first, 23 of 23)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks](https://mlsanity.com/paper/2007.04542/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks](https://mlsanity.com/paper/1905.01205/) (2019)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks](https://mlsanity.com/paper/2111.01008/) (2021)
- [Physics-informed neural networks for the shallow-water equations on the sphere](https://mlsanity.com/paper/2104.00615/) (2021)
- [PIGNet: A physics-informed deep learning model toward generalized drug-target interaction predictions](https://mlsanity.com/paper/2008.12249/) (2020)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Solving inverse-PDE problems with physics-aware neural networks](https://mlsanity.com/paper/2001.03608/) (2020)
- [Training Generative Adversarial Networks by Solving Ordinary Differential Equations](https://mlsanity.com/paper/2010.15040/) (2020)
- [Composing Partial Differential Equations with Physics-Aware Neural Networks](https://mlsanity.com/paper/2111.11798/) (2021)
- [Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2104.14320/) (2021)
- [Interval and fuzzy physics-informed neural networks for uncertain fields](https://mlsanity.com/paper/2106.13727/) (2021)
- [Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems](https://mlsanity.com/paper/2202.02710/) (2022)
- [Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2202.12358/) (2022)
- [A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency](https://mlsanity.com/paper/2210.13212/) (2022)
- [Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Support](https://mlsanity.com/paper/2206.10579/) (2022)
- [Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests](https://mlsanity.com/paper/2302.12260/) (2023)
- [High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks](https://mlsanity.com/paper/2210.00518/) (2022)
- [Physics-informed Neural Network: The Effect of Reparameterization in Solving Differential Equations](https://mlsanity.com/paper/2301.12118/) (2023)

## Built on by (most cited first, 1 of 1)

- [QGPINNs: A Physics-Informed Neural Network Framework for Nonlocal Differential Equations on Quantum Graphs](https://mlsanity.com/paper/2608.28589/) (2026)

## 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.