相关论文: Solving inverse scattering problems via reduced-or…

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of…

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost.…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…

Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

Projection-based model order reduction of an ordinary differential equation (ODE) results in a projected ODE. Based on this ODE, an existing reduced-order model (ROM) for finite volume discretizations satisfies the underlying conservation…

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…

In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the time complexity of computing the nonlinear term in a reduced…

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by…

We propose a model order reduction approach to speed up the computation of seismograms, i.e. the solution of the seismic wave equation evaluated at a receiver location, for different model parameters. Our approach achieves a reduction of…

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid…

In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…