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
Biomechanics-informed Non-rigid Medical Image Registration and its Inverse Material Property Estimation with Linear and Nonlinear Elasticity
Zhe Min, Zachary M. C. Baum, Shaheer U. Saeed, Mark Emberton, Dean C. Barratt, Zeike A. Taylor, Yipeng Hu
Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks
Xianliang Xu, Ting Du, Wang Kong, Ye Li, Zhongyi Huang
Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
Amanda A. Howard, Bruno Jacob, Sarah H. Murphy, Alexander Heinlein, Panos Stinis
Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks
Wenqian Chen, Amanda A. Howard, Panos Stinis
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis
Identification of Physical Properties in Acoustic Tubes Using Physics-Informed Neural Networks
Kazuya Yokota, Masataka Ogura, Masajiro Abe
Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks
Yianxia Qian, Yongchao Zhang, Suchuan Dong
VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior
Seungchan Ko, Sang Hyeon Park
Extremization to Fine Tune Physics Informed Neural Networks for Solving Boundary Value Problems
Abhiram Anand Thiruthummal, Sergiy Shelyag, Eun-jin Kim
FlamePINN-1D: Physics-informed neural networks to solve forward and inverse problems of 1D laminar flames
Jiahao Wu, Su Zhang, Yuxin Wu, Guihua Zhang, Xin Li, Hai Zhang