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
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
Khemraj Shukla, Zongren Zou, Chi Hin Chan, Additi Pandey, Zhicheng Wang, George Em Karniadakis
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions
Mohan Ren, Zhihao Fang, Keren Li, Anirbit Mukherjee
A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systems
Lorenzo Brevi, Antonio Mandarino, Enrico Prati
Invariant deep neural networks under the finite group for solving partial differential equations
Zhi-Yong Zhang, Jie-Ying Li, Lei-Lei Guo