  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.
