With the advances in scientific foundations and technological implementations, optical
metrology has become versatile problem-solving backbones in manufacturing, fundamental …

Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

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 …

Abstract Machine learning-based modeling of physical systems has experienced increased
interest in recent years. Despite some impressive progress, there is still a lack of …

Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

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

This open-access textbook's significant contribution is the unified derivation of data-
assimilation techniques from a common fundamental and optimal starting point, namely …

In wind farms, turbines are operated to maximize only their own power production. Individual
operation results in wake losses that reduce farm energy. Here we operate a wind turbine …

While there is currently a lot of enthusiasm about “big data”, useful data is usually “small”
and expensive to acquire. In this paper, we present a new paradigm of learning partial …

We present a physics‐informed deep neural network (DNN) method for estimating hydraulic
conductivity in saturated and unsaturated flows governed by Darcy's law. For saturated flow …