Related papers: L1-based reduced over collocation and hyper reduct…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…
In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying…
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…
The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…
We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator.…
In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…
To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…
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…
In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
Reduced-basis methods (RB methods or RBMs) form one of the most promising techniques to deliver numerical solutions of parametrized PDEs in real-time performance with reasonable accuracy. For incompressible flow problems, RBMs based on LBB…
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…
A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times…
We are concerned with employing Model Order Reduction (MOR) to efficiently solve parameterized multiscale problems using the Localized Orthogonal Decomposition (LOD) multiscale method. Like many multiscale methods, the LOD follows the idea…
Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…