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

The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-
wave analysis of electromagnetic fields in complex media and for detailed geometries …

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling.
The tremendous potential benefits of SA are, however, yet to be fully realized, both for …

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and
temporally discretization of the governing equation using polynomials into a finite …

The utilization of surrogate models to approximate complex systems has recently gained
increased popularity. Because of their capability to deal with black-box problems and lower …

The present work reviews the implementation of adaptive metamodeling for reliability
analysis with emphasis in four main types of metamodels: response surfaces, polynomial …

We are interested in the development of surrogate models for uncertainty quantification and
propagation in problems governed by stochastic PDEs using a deep convolutional encoder …

The field of machine learning (ML) has rapidly advanced the state of the art in many fields of
science and engineering, including experimental fluid dynamics, which is one of the original …

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of
numerically solving partial differential equations (PDEs) without the need of building …

We present a deep learning framework for quantifying and propagating uncertainty in
systems governed by non-linear differential equations using physics-informed neural …