In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

Well known to the machine learning community, the random feature model is a parametric
approximation to kernel interpolation or regression methods. It is typically used to …

Supervised operator learning centers on the use of training data, in the form of input-output
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …

This paper introduces a new approach for solving electrical impedance tomography (EIT)
problems using deep neural networks. The mathematical problem of EIT is to invert the …

Training nonlinear parametrizations such as deep neural networks to numerically
approximate solutions of partial differential equations is often based on minimizing a loss …

This paper introduces a meta-learning approach for parameterized pseudo-differential
operators with deep neural networks. With the help of the nonstandard wavelet form, the …

Conservation laws are considered to be fundamental laws of nature. It has broad
applications in many fields, including physics, chemistry, biology, geology, and engineering …

We introduce a novel neural network-based PDEs solver for forward and inverse problems.
The solver is grid free, mesh free, and shape free, and the solution is approximated by a …

One of the biggest challenges for simulating the Boltzmann equation is the evaluation of
fivefold collision integral. Given the recent successes of deep learning and the availability of …

This paper introduces a new approximation scheme for solving high-dimensional semilinear
partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) …