There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

In recent years, deep learning (DL) is becoming an increasingly important tool for solving
inverse scattering problems (ISPs). This paper reviews methods, promises, and pitfalls of …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image
classification. It is a simple residual network that alternates (i) a linear layer in which image …

DeepONets have recently been proposed as a framework for learning nonlinear operators
map** between infinite-dimensional Banach spaces. We analyze DeepONets and prove …

There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis
perspective. We demonstrate a very universal Frequency Principle (F-Principle)--DNNs often …

It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …

In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …

The termsurrogate modeling'in computational science and engineering refers to the
development of computationally efficient approximations for expensive simulations, such as …