The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on improving accuracy, efficiency, and applicability to complex problems. Recent developments have led to the creation of hybrid architectures, such as the combination of Fourier series and deep neural networks, which have achieved unprecedented accuracy in solving partial differential equations. Additionally, new methods have been proposed to improve the training of PINNs, including dynamic learning rate schedules and effective field theory analysis. These advancements have the potential to enable PINNs to match or exceed traditional numerical methods in various scientific computing applications. Noteworthy papers in this area include: Breaking the Precision Ceiling in Physics-Informed Neural Networks, which achieved ultra-high accuracy in solving the Euler-Bernoulli beam equation, and Analysis of Fourier Neural Operators via Effective Field Theory, which provided a principled explanation of the stability and generalization of Fourier neural operators.
Advances in Physics-Informed Neural Networks
Sources
Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO)
Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations
Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy
Explicit and Effectively Symmetric Runge-Kutta Methods
DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation
Improving Neural Network Training using Dynamic Learning Rate Schedule for PINNs and Image Classification
Analysis of Fourier Neural Operators via Effective Field Theory
Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation
A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains