相关论文: Entropy-Stable Model Reduction of One-Dimensional …
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws…
Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…
Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, however,…
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…
The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…
This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…
Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
We investigate both theoretically and numerically the consistency between the nonlinear discretization in full order models (FOMs) and reduced order models (ROMs) for incompressible flows. To this end, we consider two cases: (i) FOM-ROM…
M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
In this paper, a stabilized proper orthogonal decomposition (POD) reduced-order model (ROM) is presented for the barotropic vorticity equation. We apply the POD-ROM model to mid-latitude simplified oceanic basins, which are standard…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…