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
Physics-informed neural networks (PINNs) for numerical model error approximation and superresolution
Bozhou Zhuang, Sashank Rana, Brandon Jones, Danny Smyl
Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
Thivin Anandh, Divij Ghose, Himanshu Jain, Pratham Sunkad, Sashikumaar Ganesan, Volker John
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