Related papers: Optimal Transport for Seismic Full Waveform Invers…

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 introduce a probabilistic technique for full-waveform inversion, employing variational inference and conditional normalizing flows to quantify uncertainty in migration-velocity models and its impact on imaging. Our approach integrates…

We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…

Full waveform inversion (FWI) is one of a family of methods that allows the reconstruction of earth subsurface parameters from measurements of waves at or near the surface. This is a numerical optimization problem that uses the whole…

Full Waveform Inversion (FWI) is an important geophysical technique considered in subsurface property prediction. It solves the inverse problem of predicting high-resolution Earth interior models from seismic data. Traditional FWI methods…

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…

It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…

Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…

Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties.…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…

Full waveform inversion (FWI) is a process in which seismic numerical simulations are fit to observed data by changing the wave velocity model of the medium under investigation. The problem is non-linear, and therefore optimization…

Remote sensing observations from satellites and global biogeochemical models have combined to revolutionize the study of ocean biogeochemical cycling, but comparing the two data streams to each other and across time remains challenging due…

Full waveform inversion (FWI) is a high-resolution seismic inversion technique popularly used in oil and gas exploration. Traditional FWI employs the $l_2$ norm measurement to minimize the misfit between observed and predicted seismic data.…

We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant…

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…

This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport.…

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…

We explore the geometry of the Bures-Wasserstein space for potentially degenerate Gaussian measures on a separable Hilbert space. In this general setting, the optimal transport map is formally the subgradient of a convex function that is…

Full waveform inversion (FWI) is an iterative identification process that serves to minimize the misfit of model-based simulated and experimentally measured wave field data, with the goal of identifying a field of parameters for a given…