We propose a general---ie, independent of the underlying equation---registration method for
parameterized model order reduction. Given the spatial domain Ω⊂R^d and the manifold …

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 …

We present a nonlinear interpolation technique for parametric fields that exploits optimal
transportation of coherent structures of the solution to achieve accurate performance. The …

We propose an automated nonlinear model reduction and mesh adaptation framework for
rapid and reliable solution of parameterized advection-dominated problems, with emphasis …

We propose a model reduction procedure for rapid and reliable solution of parameterized
hyperbolic partial differential equations. Due to the presence of parameter-dependent shock …

We present a general (ie, independent of the underlying model) interpolation technique
based on optimal transportation of Gaussian models for parametric advection-dominated …

We propose a nonlinear registration-based model reduction procedure for rapid and reliable
solution of parameterized two-dimensional steady conservation laws. This class of problems …

We develop and analyze a parametric registration procedure for manifolds associated with
the solutions to parametric partial differential equations in two-dimensional domains. Given …

Advection-dominated problems are commonly noticed in nature, engineering systems, and a
wide range of industrial processes. For these problems, linear approximation methods …