Registration-based model reduction of parameterized two-dimensional conservation laws
arXiv:2105.02024 · doi:10.1016/j.jcp.2022.111068
Abstract
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 is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent discontinuities that cannot be adequately represented through linear approximation spaces. Our approach builds on a general (i.e., independent of the underlying equation) registration procedure for the computation of a mapping that tracks moving features of the solution field and on an hyper-reduced least-squares Petrov-Galerkin reduced-order model for the rapid and reliable computation of the solution coefficients. The contributions of this work are twofold. First, we investigate the application of registration-based methods to two-dimensional hyperbolic systems. Second, we propose a multi-fidelity approach to reduce the offline costs associated with the construction of the parameterized mapping and the reduced-order model. We discuss the application to an inviscid supersonic flow past a parameterized bump, to illustrate the many features of our method and to demonstrate its effectiveness.
arXiv comment22 pages, 11 figures
References in corpus (18)
- Adaptive -refinement for reduced-order models
- An introduction to sampling via measure transport
- The method of freezing as a new tool for nonlinear reduced basis approximation of parameterized evolution equations
- An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
- Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
- Generating Random Earthquake Events for PTHA
- Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations
- Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces
- Entropy stable reduced order modeling of nonlinear conservation laws
- Online adaptive basis refinement and compression for reduced-order models via vector-space sieving
- Reduced Basis Methods: Success, Limitations and Future Challenges
- Efficient nonlinear manifold reduced order model
- (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
- Basic Ideas and Tools for Projection-Based Model Reduction of Parametric Partial Differential Equations
- Expressivity of Deep Neural Networks
- Registration-based model reduction in complex two-dimensional geometries
- A discretize-then-map approach for the treatment of parameterized geometries in model order reduction
- Data-Driven Snapshot Calibration via Monotonic Feature Matching