Related papers: Adaptive hyper-reduction of non-sparse operators: …
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
This paper presents a method of data-driven parametric Dynamic Mode Decomposition (p-DMD) to derive a linear parameter-varying reduced-order model (LPV-ROM) for the nonlinear aeroelasticity of highly flexible aircraft. It directly uses the…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…
This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The Convected Scheme (CS) is a `forward-trajectory' semi-Lagrangian method for solution of transport equations, which has been most often applied to the kinetic description of plasmas and rarefied neutral gases. In its simplest form, the CS…
This paper suggests a nonparametric scheme to find the sparse solution of the underdetermined system of linear equations in the presence of unknown impulsive or non-Gaussian noise. This approach is robust against any variations of the noise…
We present a dequantization algorithm for the Vlasov--Poisson (VP) system, termed the dequantized particle algorithm, by systematically dequantizing the underlying many-body quantum theory. Starting from the second-quantized Hamiltonian…
The present paper describes a parallel unstructured-mesh Plasma simulation code based on Finite Volume method. The code dynamically refines and coarses mesh for accurate resolution of the different features regarding the electron density.…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…