# Exploring Physics-Informed Neural Networks: From Fundamentals to Applications in Complex Systems

arXiv: https://arxiv.org/abs/2410.00422 · HTML: https://mlsanity.com/paper/2410.00422/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2024.

## Built on by (most cited first, 2 of 2)

- [Topological Signatures of ReLU Neural Network Activation Patterns](https://mlsanity.com/paper/2510.12700/) (2025)
- [A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization](https://mlsanity.com/paper/2602.13811/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of PINNs, tracing their evolution, modifications, and various variants. It explores the impact of different parameters on PINNs and the optimization algorithms involved. The review also delves into the theoretical advancements related to the convergence, consistency, and stability of numerical solutions using PINNs, while highlighting the current state of the art. Given their ability to address equations involving complex physics, the article discusses various applications of PINNs, with a particular focus on their utility in computational fluid dynamics problems. Additionally, it identifies current gaps in the research and outlines future directions for the continued development of PINNs.