A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
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 …
physical simulations in which the intrinsic solution space falls into a subspace with a small …
Reduced basis methods for time-dependent problems
Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …
study of real-world phenomena in applied science and engineering. Computational methods …
Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling
B Peherstorfer - SIAM Journal on Scientific Computing, 2020 - SIAM
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 …
propagate over time, such as convection-dominated flows and wave-type phenomena …
The shifted proper orthogonal decomposition: A mode decomposition for multiple transport 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 …
reduction approaches. We present a model reduction method, which is suited for these kinds …
SVD perspectives for augmenting DeepONet flexibility and interpretability
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 …
attracting attention in multiple fields due to their utility for fast and accurate emulation of …
The neural network shifted-proper orthogonal decomposition: a machine learning approach for non-linear reduction of hyperbolic equations
Abstract Models with dominant advection always posed a difficult challenge for projection-
based reduced order modelling. Many methodologies that have recently been proposed are …
based reduced order modelling. Many methodologies that have recently been proposed are …
On the role of nonlinear correlations in reduced-order modelling
This work investigates nonlinear dimensionality reduction as a means of improving the
accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear …
accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear …
Reduced order models for Lagrangian hydrodynamics
As a mathematical model of high-speed flow and shock wave propagation in a complex
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …
Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking
MA Mirhoseini, MJ Zahr - Journal of Computational Physics, 2023 - Elsevier
This work introduces a new approach to reduce the computational cost of solving partial
differential equations (PDEs) with convection-dominated solutions: model reduction with …
differential equations (PDEs) with convection-dominated solutions: model reduction with …
Efficient nonlinear manifold reduced order model
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 …
physical simulations, in which the intrinsic solution space falls into a subspace with a small …