The field of physics-informed neural operators and numerical methods is rapidly advancing, with a focus on developing more efficient and accurate methods for solving partial differential equations (PDEs) and other complex problems. Recent research has led to the development of new neural operator architectures, such as the Hilbert Neural Operator and the U-shaped Physics-Informed Network, which have shown promising results in modeling complex systems and phenomena. Additionally, advances in numerical methods, such as the Separated-Variable Spectral Neural Networks and the Goal-Oriented Adaptive Finite Element Multilevel Quasi-Monte Carlo, have improved the accuracy and efficiency of PDE solvers. These developments have the potential to impact a wide range of fields, including scientific computing, engineering, and physics. Noteworthy papers include the introduction of DINOZAUR, a diffusion-based neural operator parametrization with uncertainty quantification, and the development of QuadrANN, a Graph Neural Network architecture designed to learn optimal quadrature weights directly from the underlying geometry of point clouds.
Advances in Physics-Informed Neural Operators and Numerical Methods
Sources
Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators
Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs
When surface evolution meets Fokker-Planck equation: a novel tangential velocity model for uniform parametrization
Goal-Oriented Adaptive Finite Element Multilevel Quasi-{M}onte {C}arlo
U-PINet: End-to-End Hierarchical Physics-Informed Learning With Sparse Graph Coupling for 3D EM Scattering Modeling
Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Network
BubbleONet: A Physics-Informed Neural Operator for High-Frequency Bubble Dynamics
Tunable Plasmonic Absorption in Metal-Dielectric Multilayers via FDTD Simulations and an Explainable Machine Learning Approach
Optimal Design of Broadband Absorbers with Multiple Plasmonic Nanoparticles via Reduced Basis Method
Hilbert Neural Operator: Operator Learning in the Analytic Signal Domain
An Improved Physically-Based Surface Triangulation Method
Toroidal area-preserving parameterizations of genus-one closed surfaces
Learning Geometric-Aware Quadrature Rules for Functional Minimization