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 …

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 …

Physics-informed neural networks (PINNs) have gained popularity across different
engineering fields due to their effectiveness in solving realistic problems with noisy data and …

Accurate solutions to inverse supersonic compressible flow problems are often required for
designing specialized aerospace vehicles. In particular, we consider the problem where we …

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

We develop a distributed framework for the physics-informed neural networks (PINNs)
based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs …

Physics-informed neural networks (PINNs) are successful machine-learning methods for the
solution and identification of partial differential equations. We employ PINNs for solving the …

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm
for solving problems relating to differential equations. Compared to classical numerical …

The velocities measured by particle image velocimetry (PIV) and particle tracking
velocimetry (PTV) commonly provide sparse information on flow motions. A dense velocity …