Related papers: Reduced Order Modeling for First Order Hyperbolic …
Full waveform inversion (FWI) aims at estimating subsurface medium properties from measured seismic data. It is usually cast as a non-linear least-squares problem that incorporates uncertainties in the measurements. In exploration…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
Full waveform inversion (FWI) is beginning to be used to characterize weak seismic events at different scales, an example of which is microseismic event (MSE) characterization. However, FWI with unknown sources is a severely underdetermined…
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger…
Full waveform inversion (FWI) is an iterative nonlinear waveform matching procedure subject to wave-equation constraint. FWI is highly nonlinear when the wave-equation constraint is enforced at each iteration. To mitigate nonlinearity,…
Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…
Full waveform inversion (FWI) commonly stands for the state-of-the-art approach for imaging subsurface structures and physical parameters, however, its implementation usually faces great challenges, such as building a good initial model to…
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…
Full waveform inversion (FWI) is a nonlinear waveform matching procedure, which suffers from cycle skipping when the initial model is not kinematically-accurate enough. To mitigate cycle skipping, wavefield reconstruction inversion (WRI)…
Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise,…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…
Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…
We consider the high-resolution seismic imaging method called full-waveform inversion (FWI). FWI is a data fitting method aimed at inverting for subsurface mechanical parameters. Despite the large adoption of FWI by the academic and…
The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar imaging. One specification of this approach is that it…
Full waveform inversion is a high-resolution subsurface imaging technique, in which full seismic waveforms are used to infer subsurface physical properties. We present a novel, target-enclosing, full-waveform inversion framework based on an…
Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Hamiltonian operator inference has been developed 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. The method…
Full-Waveform Inversion (FWI) is a high-resolution technique used in geophysics to evaluate the physical parameters and construct subsurface models in a noisy and limited data scenario. The ill-posed nature of the FWI turns this a…