A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

Reduced order modeling (ROM) has been widely used to create lower order,
computationally inexpensive representations of higher-order dynamical systems. Using …

We study the performance of long short-term memory networks (LSTMs) and neural ordinary
differential equations (NODEs) in learning latent-space representations of dynamical …

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in
the design of commercial air transportation vehicles. Computational fluid dynamics models …

This work introduces a new approach to reduce the computational cost of solving partial
differential equations (PDEs) with convection-dominated solutions: model reduction with …

Generating a digital twin of any complex system requires modeling and computational
approaches that are efficient, accurate, and modular. Traditional reduced order modeling …

Digital twins have emerged as a key technology for optimizing the performance of
engineering products and systems. High-fidelity numerical simulations constitute the …

Purpose Three‐dimensional, time‐resolved blood flow measurement (4D‐flow) is a powerful
research and clinical tool, but improved resolution and scan times are needed. Therefore …

We present a numerical method to efficiently solve optimization problems governed by large-
scale nonlinear systems of equations, including discretized partial differential equations …

This work proposes a machine-learning framework for modeling the error incurred by
approximate solutions to parameterized dynamical systems. In particular, we extend the …