Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation

2025/06/16 by Koji Kobayashi, Kobayashi, Koji, Tomi Ohtsuki +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Matrix Theory and Algorithms #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

paper · pdf · doi:10.48550/arxiv.2506.13210

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

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.

Citations

• Diffusion model for analyzing quantum fingerprints in conductance fluctuation
• Large-Angle Convergent-Beam Electron Diffraction Patterns via Conditional Generative Adversarial Networks
• Automatic Differentiation for Inverse Problems with Applications in Quantum Transport
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Related

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