Advances in physics-informed neural networks

Abstract

In recent years, deep neural networks have demonstrated remarkable success in such diverse fields as computer vision, natural language processing, game theory, revolutionizing approaches to categorization, pattern recognition, and regression tasks. Among recent developments in scientific machine learning, Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving ordinary and partial differential equations using sparse data. Since their introduction in 2017 [1], significant progress has been made in optimizing PINNs through advancements in network architectures, adaptive refinement, domain decomposition, and adaptive activation functions. A notable innovation is the Physics-Informed Kolmogorov-Arnold Networks (PIKANs) [2], which build on Kolmogorov’s representation theory to offer an alternative to conventional PINNs. In this presentation, we discuss recent PINN advancements, focusing on architectural improvements, feature expansion, optimization strategies, uncertainty quantification, and theoretical foundations. We also examine existing computational frameworks and software tools [3] solving several problems from fluid mechanics and chemical engineering.