相关论文: Model Reduction for Transport-Dominated Problems v…

In this work we focus on reduced order modelling for problems for which the resulting reduced basis spaces show a slow decay of the Kolmogorov $n$-width, or, in practical calculations, its computational surrogate given by the magnitude of…

Reduced-order models (ROMs) remain generally unreliable for convection-dominated problems, such as those encountered in hypersonic flows, due to the slowly decaying Kolmogorov $n$-width of linear subspace approximations, known as the…

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. Traditional model reduction methods have difficulties with these…

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…

This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…

The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

The Kolmogorov $n$-width is an established benchmark to judge the performance of reduced basis and similar methods that produce linear reduced spaces. Although immensely successful in the elliptic regime, this width, shows unsatisfactory…

Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by…