Reconstructing the Magnetic Field in an Arbitrary Domain via Data-driven Bayesian Methods and Numerical Simulations

TL;DR

This paper presents a Bayesian data-driven algorithm for reconstructing magnetic fields in arbitrary domains, effectively solving inverse problems with uncertain boundary conditions through numerical optimization.

Contribution

It introduces a novel Bayesian framework combined with numerical simulations to accurately recover magnetic fields in complex geometries, advancing inverse problem solutions.

Findings

Successful reconstruction of magnetic fields in a conical domain

High accuracy in parameter recovery demonstrated

Effective handling of uncertain boundary conditions

Abstract

Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in deducing the most probable parameter values that align with the collected data. This study introduces an algorithm for reconstructing parameters by addressing an inverse problem formulated through differential equations underpinned by uncertain boundary conditions or variant parameters. We adopt a Bayesian approach for parameter inference, delineating the establishment of prior, likelihood, and posterior distributions, and the subsequent resolution of the maximum a posteriori problem via numerical optimization techniques. The proposed algorithm is applied to the task of magnetic field reconstruction within a conical domain, demonstrating precise recovery of the true parameter values.