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
Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution
Justice Mason, Christine Allen-Blanchette, Nicholas Zolman, Elizabeth Davison, Naomi Ehrich Leonard
Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex Geometries
Zhiwei Fang, Sifan Wang, Paris Perdikaris
Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks
T. Sahin, M. von Danwitz, A. Popp
Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, Ding-Xuan Zhou
Physics-Informed Boundary Integral Networks (PIBI-Nets): A Data-Driven Approach for Solving Partial Differential Equations
Monika Nagy-Huber, Volker Roth
HyperLoRA for PDEs
Ritam Majumdar, Vishal Jadhav, Anirudh Deodhar, Shirish Karande, Lovekesh Vig, Venkataramana Runkana