The computerized simulations of physical and socio-economic systems have proliferated in
the past decade, at the same time, the capability to develop high-fidelity system predictive …

Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Data scarcity is a major challenge when training deep learning (DL) models. DL demands a
large amount of data to achieve exceptional performance. Unfortunately, many applications …

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented
attention because of its promise to further optimize process design, quality control, health …

Recent work in scientific machine learning has developed so-called physics-informed neural
network (PINN) models. The typical approach is to incorporate physical domain knowledge …

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 …

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

Despite the significant progress over the last 50 years in simulating flow problems using
numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate …

On top of machine learning (ML) models, uncertainty quantification (UQ) functions as an
essential layer of safety assurance that could lead to more principled decision making by …

It is widely known that neural networks (NNs) are universal approximators of continuous
functions. However, a less known but powerful result is that a NN with a single hidden layer …