Physic Informed Neural Network
Physics-informed neural networks (PINNs) integrate physical laws, typically expressed as differential equations, into neural network training to solve complex scientific problems. Current research focuses on improving PINN accuracy and efficiency through architectural innovations like Fourier-based networks, Kolmogorov-Arnold networks, and wavelet-based approaches, as well as advanced optimization strategies such as dual cone gradient descent and DiffGrad. These advancements aim to overcome limitations in handling high-frequency solutions, complex geometries, and stiff equations, ultimately enhancing the applicability of PINNs across diverse scientific and engineering domains, including fluid dynamics, seismology, and materials science.
Papers
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese, Zongren Zou, Nazanin Ahmadi Daryakenari, Chenxi Wu, George Em Karniadakis
Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneity
Handi Zhang, Langchen Liu, Lu Lu
Deep Learning Alternatives of the Kolmogorov Superposition Theorem
Leonardo Ferreira Guilhoto, Paris Perdikaris
Towards Model Discovery Using Domain Decomposition and PINNs
Tirtho S. Saha, Alexander Heinlein, Cordula Reisch
Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networks
Marcus Haywood-Alexander, Giacomo Arcieri, Antonios Kamariotis, Eleni Chatzi