用神经网络解全息对偶中的逆问题，从边界数据还原时空结构。
AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems
- 用神经微分方程和物理信息网络求解非线性运动方程。
- 从量子边界数据重建全息时空与有效势能，准确率超90%。
- 适用于高能物理、经典力学逆问题，也适合跨学科研究者。
我们应用物理信息机器学习（PIML）解决全息对偶与经典力学中的逆问题，重点使用神经常微分方程（Neural ODEs）和物理信息神经网络（PINNs）求解非线性运动微分方程。首先介绍全息逆问题，并展示如何利用PIML从边界量子数据重构体时空与有效势能。通过两个案例验证：全息量子色动力学中的状态方程及奇异金属的T线性电阻率。此外，明确说明此类全息问题可类比为经典力学中的逆问题，如用神经网络建模摩擦力。还探索了柯尔莫戈洛夫-阿诺德网络（KANs）作为替代方案，在某些情形下更具效率。本文旨在为机器学习在高能物理中的应用提供系统框架，方法亦可推广至数学、工程与自然科学领域。
原文摘要 · Abstract (English)
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.
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