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 …

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

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 …

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 …

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 …

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this
date PINNs have not been successful in simulating dynamical systems whose solution …

Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics,
thermal/electronic transport, electromagnetism, and optics. Topology optimization is an …

Here we propose a generalized space-time domain decomposition approach for the physics-
informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on …

Abstract Machine learning (ML) has been increasingly used to aid aerodynamic shape
optimization (ASO), thanks to the availability of aerodynamic data and continued …