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

Fracture is one of the most commonly encountered failure modes of engineering materials
and structures. Prevention of cracking-induced failure is, therefore, a major concern in …

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

Harnessing modern parallel computing resources to achieve complex multiphysics
simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment …

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often
considered as supervised learning problems where input and output data pairs are used for …

Supervised operator learning is an emerging machine learning paradigm with applications
to modeling the evolution of spatio-temporal dynamical systems and approximating general …

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 …

MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite
element methods that features arbitrary high-order finite element meshes and spaces …

Partial differential equations play a fundamental role in the mathematical modelling of many
processes and systems in physical, biological and other sciences. To simulate such …

Data-driven learning of partial differential equations' solution operators has recently
emerged as a promising paradigm for approximating the underlying solutions. The solution …