Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation

TL;DR

Backsolution introduces a versatile framework for solving inverse problems using automatic differentiation, applicable to various fields, demonstrated by reconstructing conductor profiles from magnetotransport data.

Contribution

The paper presents a general framework leveraging automatic differentiation for inverse problems, enabling accurate reconstruction and reverse modeling in physics.

Findings

Successfully reconstructs spatial profiles from magnetotransport measurements.

Framework is broadly applicable to inverse problems in physics.

Enables effective reverse modeling even with incomplete data.

Abstract

We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical simulator is available. As a concrete example, we demonstrate that our method can accurately reconstruct the spatial profiles in a conductor from magnetotransport measurements. Even if the given data are insufficient to uniquely determine the profiles, the same framework enables effective reverse modeling. This method is general, flexible, and readily adaptable to a broad class of inverse problems across condensed matter physics and beyond.