Related papers: Robust Model Reduction Of Hyperbolic Problems by $…
Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…
We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer.…
We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric…
We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…
In this contribution we consider localized, robust and efficient a-posteriori error estimation of the localized reduced basis multi-scale (LRBMS) method for parametric elliptic problems with possibly heterogeneous diffusion coefficient. The…
We construct a least squares approximation method for the recovery of complex-valued functions from a reproducing kernel Hilbert space on $D \subset \mathbb{R}^d$. The nodes are drawn at random for the whole class of functions and the error…
In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process.…
We consider the problem of maximizing the multilinear extension of a submodular function subject a single matroid constraint or multiple packing constraints with a small number of adaptive rounds of evaluation queries. We obtain the first…
This study proposes an intrusive projection-based model-order reduction framework for nonlinear problems with a polynomial structure, solved iteratively using a Newton solver in the reduced space. It is demonstrated that for the targeted…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model results in an index-1 hyperbolic, differential algebraic equation quadratic in state,…
We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in…
A new type of systematic approach to study the incompressible Euler equations numerically via the vanishing viscosity limit is proposed in this work. We show the new strategy is unconditionally stable that the $L^2$-energy dissipates and…
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…
In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…
Several reduced order models have been developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…