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
ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations
Vladislav Trifonov, Alexander Rudikov, Oleg Iliev, Ivan Oseledets, Ekaterina Muravleva
Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems
Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Antareep Kumar Sarma
Element-wise Multiplication Based Deeper Physics-Informed Neural Networks
Feilong Jiang, Xiaonan Hou, Min Xia
Chebyshev Spectral Neural Networks for Solving Partial Differential Equations
Pengsong Yin, Shuo Ling, Wenjun Ying
Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheology
Sukirt Thakur, Harsa Mitra, Arezoo M. Ardekani
Solving Differential Equations using Physics-Informed Deep Equilibrium Models
Bruno Machado Pacheco, Eduardo Camponogara
Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)
Chenhao Si, Ming Yan
Multivariate Physics-Informed Convolutional Autoencoder for Anomaly Detection in Power Distribution Systems with High Penetration of DERs
Mehdi Jabbari Zideh, Sarika Khushalani Solanki
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang, Zongren Zou, George Em Karniadakis
Closed-form Symbolic Solutions: A New Perspective on Solving Partial Differential Equations
Shu Wei, Yanjie Li, Lina Yu, Min Wu, Weijun Li, Meilan Hao, Wenqiang Li, Jingyi Liu, Yusong Deng
RoPINN: Region Optimized Physics-Informed Neural Networks
Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, Mingsheng Long
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations
Wenrui Hao, Xinliang Liu, Yahong Yang