This article presents two new non-intrusive reduced order models based upon proper
orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of …

We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic
partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic …

This is part II of our paper in which we propose and develop a dynamically bi-orthogonal
method (DyBO) to study a class of time-dependent stochastic partial differential equations …

Reduced order models (ROMs) have become prevalent in many fields of physics as they
offer the potential to simulate dynamical systems with substantially increased computation …

We propose a data-driven stochastic method (DSM) to study stochastic partial differential
equations (SPDEs) in the multiquery setting. An essential ingredient of the proposed method …