AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems

TL;DR

This paper demonstrates how physics-informed neural networks and neural ODEs can solve complex inverse problems in holography and classical mechanics, reconstructing physical parameters from boundary data with improved efficiency.

Contribution

It introduces a systematic framework applying neural network-based approaches, including Neural ODEs, PINNs, and Kolmogorov-Arnold Networks, to inverse problems in holography and mechanics.

Findings

Successful reconstruction of bulk spacetime and potentials from boundary data.

Application of neural networks to model frictional forces in classical mechanics.

Introduction of Kolmogorov-Arnold Networks as efficient alternatives.

Abstract

We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving non-linear differential equations of motion. First, we introduce holographic inverse problems and demonstrate how PIML can reconstruct bulk spacetime and effective potentials from boundary quantum data. To illustrate this, two case studies are explored: the QCD equation of state in holographic QCD and $T$-linear resistivity in holographic strange metals. Additionally, we explicitly show how such holographic problems can be analogized to inverse problems in classical mechanics, modeling frictional forces with neural networks. We also explore Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks, offering more efficient solutions in certain cases. This manuscript aim to provide a systematic framework for using neural networks in inverse problems, serving as a comprehensive reference for researchers in machine learning for high-energy physics, with methodologies that also have broader applications in mathematics, engineering, and the natural sciences.