705 citations · 843 across the 9 of their papers we have counts for
7 papers · 1 filter
Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics
Hanwen Wang, Paris Perdikaris
Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of standard coordinate networks:…
Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers
Shyam Sankaran, Hanwen Wang, Paris Perdikaris
Neural PDE solvers have followed the scaling trajectory of vision and language, with recent foundation models reaching billions of parameters. We argue that scale is a poor substit…
CViT: Continuous Vision Transformer for Operator Learning
Sifan Wang, Jacob H Seidman, Shyam Sankaran +3
Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various…
An Expert's Guide to Training Physics-informed Neural Networks
Sifan Wang, Shyam Sankaran, Hanwen Wang +1
Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE…
Improved architectures and training algorithms for deep operator networks
Sifan Wang, Hanwen Wang, Paris Perdikaris
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can…
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets
Sifan Wang, Hanwen Wang, Paris Perdikaris
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach…
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Sifan Wang, Hanwen Wang, Paris Perdikaris
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cas…