AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems
It provides a systematic framework for researchers in high-energy physics and related fields to use neural networks in inverse problems, with broader applications in mathematics, engineering, and natural sciences.
The paper tackles inverse problems in holography and classical mechanics by applying physics-informed machine learning (PIML) with neural networks, demonstrating reconstruction of bulk spacetime and effective potentials from boundary data in case studies like QCD equation of state and T-linear resistivity, and showing how these problems analogize to classical mechanics with frictional forces.
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.