Data completion and stochastic algorithms for PDE inversion problems with many measurements

TL;DR

This paper introduces a data completion method to improve PDE inversion with many measurements, enabling efficient stochastic algorithms by approximating missing data across experiments with different receiver locations.

Contribution

It proposes a novel data completion approach for PDE inverse problems with non-shared receivers, enhancing computational efficiency in stochastic algorithms.

Findings

Data completion improves PDE inversion efficiency.

Completed data enables faster stochastic algorithms.

Method compares favorably to random subset approach.

Abstract

Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic and deterministic, to reduce this computational burden, assuming that all experiments share the same set of receivers. In the present article we consider the more general and practically important case where receivers are not shared across experiments. We propose a data completion approach to alleviate this problem. This is done by means of an approximation using an appropriately restricted gradient or Laplacian regularization, extending existing data for each experiment to the union of all receiver locations. Results using the method of simultaneous sources (SS) with the completed data are then compared to those obtained by a more general but slower random subset (RS) method which requires no modifications.