# Space-time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

@article{Choi2019SpacetimeRO, title={Space-time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems}, author={Youngsoo Choi and Peter N. Brown and Bill Arrighi and Robert Anderson}, journal={J. Comput. Phys.}, year={2019}, volume={424}, pages={109845} }

## 33 Citations

### Efficient space-time reduced order model for linear dynamical systems in Python using less than 120 lines of code

- Computer ScienceMathematics
- 2021

This work presents for the first time the derivation of the space-time Petrov-Galerkin projection for linear dynamical systems and its corresponding block structures and derives an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.

### Space-time reduced basis methods for parametrized unsteady Stokes equations

- Computer ScienceArXiv
- 2022

This work analyzes space–time reduced basis methods for the efﬁcient numerical simulation of hæmodynamics in arteries to investigate the application of ST–RB methods to the unsteady incompressible Stokes equations, with a particular focus on stability.

### Windowed space–time least-squares Petrov–Galerkin model order reduction for nonlinear dynamical systems

- Computer Science
- 2021

### Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

- Computer ScienceEnergies
- 2021

To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for keff and by one order of magnitude by the scalar flux.

### Reduced order models for Lagrangian hydrodynamics

- Environmental Science, MathematicsComputer Methods in Applied Mechanics and Engineering
- 2022

### Local Lagrangian reduced-order modeling for Rayleigh-Taylor instability by solution manifold decomposition

- PhysicsJournal of Computational Physics
- 2023

### Projection-based model reduction of dynamical systems using space–time subspace and machine learning

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2021

### Efficient nonlinear manifold reduced order model

- Computer ScienceArXiv
- 2020

An efficient nonlinear manifold ROM (NM-ROM) is developed, which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs and shows that neural networks can learn a more efficient latent space representation on advection-dominated data from 2D Burgers' equations with a high Reynolds number.

### A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations

- Computer ScienceJ. Comput. Phys.
- 2021

### A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation

- Computer ScienceArXiv
- 2022

A novel RBM to construct ROM for the time-dependent RTE based on the micro-macro decomposition, which can be readily incorporated into multi-query scenarios to accelerate problems arising from uncertainty quantiﬁcation, control, inverse problems and optimization.

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