用机器学习同时发现物理概念和方程，模拟人类科学发现过程。
Discover physical concepts and equations with machine learning
- 结合变分自编码器与神经微分方程，实现物理概念与方程的联合发现。
- 在多个经典物理案例中成功复现了日心说、万有引力等正确理论。
- 适合对物理规律自动发现感兴趣的科研人员或交叉学科研究者。
当已有部分先验知识时，机器学习可揭示物理概念或物理方程。然而，这两者常相互交织，难以独立发现。本文扩展了模拟人类物理推理过程的SciNet神经网络架构，提出一种融合变分自编码器（VAE）与神经微分方程（Neural ODEs）的模型，能够从不同物理系统的仿真实验数据中同步发现物理概念与支配性方程。该方法应用于多个受物理学史启发的案例，包括哥白尼的日心说、牛顿万有引力定律、薛定谔波动力学及泡利的自旋-磁矩关系。结果表明，正确的物理理论可在神经网络中自然涌现。
原文摘要 · Abstract (English)
Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined and cannot be discovered independently. We extend SciNet, which is a neural network architecture that simulates the human physical reasoning process for physics discovery, by proposing a model that combines Variational Autoencoders (VAE) with Neural Ordinary Differential Equations (Neural ODEs). This allows us to simultaneously discover physical concepts and governing equations from simulated experimental data across various physical systems. We apply the model to several examples inspired by the history of physics, including Copernicus' heliocentrism, Newton's law of gravity, Schrödinger's wave mechanics, and Pauli's spin-magnetic formulation. The results demonstrate that the correct physical theories can emerge in the neural network.
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