Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate
physical simulations in which the intrinsic solution space falls into a subspace with a small …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

This work presents a model reduction approach for problems with coherent structures that
propagate over time, such as convection-dominated flows and wave-type phenomena …

Transport-dominated phenomena provide a challenge for common mode-based model
reduction approaches. We present a model reduction method, which is suited for these kinds …

Deep operator networks (DeepONets) are powerful and flexible architectures that are
attracting attention in multiple fields due to their utility for fast and accurate emulation of …

Abstract Models with dominant advection always posed a difficult challenge for projection-
based reduced order modelling. Many methodologies that have recently been proposed are …

As a mathematical model of high-speed flow and shock wave propagation in a complex
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …

This work investigates nonlinear dimensionality reduction as a means of improving the
accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear …

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

A new model order reduction approach is proposed for parametric steady‐state nonlinear
fluid flows characterized by shocks and discontinuities whose spatial locations and …