用深度学习从向量场反推哈密顿函数，实现自动发现物理规律。
SymFlux: deep symbolic regression of Hamiltonian vector fields
- 混合CNN-LSTM架构学习向量场并输出符号表达式
- 在自建数据集上准确恢复哈密顿函数的数学形式
- 适合对物理规律自动化发现感兴趣的科研人员
我们提出SymFlux，一种新型深度学习框架，用于在标准辛平面上从对应向量场进行符号回归，识别哈密顿函数。SymFlux模型采用混合CNN-LSTM架构，学习并输出底层哈密顿函数的符号数学表达式。训练与验证基于本研究新构建的哈密顿向量场数据集，这是本文的关键贡献之一。实验结果表明，该模型能有效准确地恢复这些符号表达式，推动了哈密顿力学中的自动化发现进程。
原文摘要 · Abstract (English)
We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM architectures to learn and output the symbolic mathematical expression of the underlying Hamiltonian. Training and validation are conducted on newly developed datasets of Hamiltonian vector fields, a key contribution of this work. Our results demonstrate the model's effectiveness in accurately recovering these symbolic expressions, advancing automated discovery in Hamiltonian mechanics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。