Sampling weights of deep neural networks
We introduce a probability distribution, combined with an efficient sampling algorithm, for
weights and biases of fully-connected neural networks. In a supervised learning context, no …
weights and biases of fully-connected neural networks. In a supervised learning context, no …
Data-efficient operator learning via unsupervised pretraining and in-context learning
Recent years have witnessed the promise of coupling machine learning methods and
physical domain-specific insights for solving scientific problems based on partial differential …
physical domain-specific insights for solving scientific problems based on partial differential …
Learning integral operators via neural integral equations
Nonlinear operators with long-distance spatiotemporal dependencies are fundamental in
modelling complex systems across sciences; yet, learning these non-local operators …
modelling complex systems across sciences; yet, learning these non-local operators …
Group equivariant fourier neural operators for partial differential equations
We consider solving partial differential equations (PDEs) with Fourier neural operators
(FNOs), which operate in the frequency domain. Since the laws of physics do not depend on …
(FNOs), which operate in the frequency domain. Since the laws of physics do not depend on …
Neural spectral methods: Self-supervised learning in the spectral domain
We present Neural Spectral Methods, a technique to solve parametric Partial Differential
Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal …
Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal …
Memory-less scattering imaging with ultrafast convolutional optical neural networks
The optical memory effect in complex scattering media including turbid tissue and speckle
layers has been a critical foundation for macroscopic and microscopic imaging methods …
layers has been a critical foundation for macroscopic and microscopic imaging methods …
How Expressive are Spectral-Temporal Graph Neural Networks for Time Series Forecasting?
Spectral-temporal graph neural network is a promising abstraction underlying most time
series forecasting models that are based on graph neural networks (GNNs). However, more …
series forecasting models that are based on graph neural networks (GNNs). However, more …
Neural integral equations
Nonlinear operators with long distance spatiotemporal dependencies are fundamental in
modeling complex systems across sciences, yet learning these nonlocal operators remains …
modeling complex systems across sciences, yet learning these nonlocal operators remains …
Learning space-time continuous latent neural pdes from partially observed states
We introduce a novel grid-independent model for learning partial differential equations
(PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a …
(PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a …
Understanding the Expressivity and Trainability of Fourier Neural Operator: A Mean-Field Perspective
In this paper, we explores the expressivity and trainability of the Fourier Neural Operator
(FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random …
(FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random …