用SVD改进神经网络，更轻量且抗噪地发现动力系统守恒量
Constants of motion network revisited
- 基于奇异值分解构建新网络架构，提升守恒量学习能力
- 在非哈密顿系统上表现更优，参数量减少且抗噪声更强
- 适合需要高效、鲁棒守恒量发现的研究者使用
发现动力系统的守恒量对理解其行为具有重要意义，但传统方法依赖高深数学知识与敏锐分析力。随着深度学习的发展，基于神经网络的方法（如常量守恒网络COMET）展现出潜力。尽管COMET能通过发现守恒量提升动力学预测性能，仍有优化空间。本文提出一种基于奇异值分解（SVD）的新神经网络架构及双阶段训练算法，显著提升COMET性能。实验表明，新方法不仅保留COMET可应用于非哈密顿系统、能指示守恒量数量的优势，还更轻量、更具抗噪性。
原文摘要 · Abstract (English)
Discovering constants of motion is meaningful in helping understand the dynamical systems, but inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant Of Motion nETwork (COMET), are promising in handling this scientific problem. Although the COMET method can produce better predictions on dynamics by exploiting the discovered constants of motion, there is still plenty of room to sharpen it. In this paper, we propose a novel neural network architecture, built using the singular-value-decomposition (SVD) technique, and a two-phase training algorithm to improve the performance of COMET. Extensive experiments show that our approach not only retains the advantages of COMET, such as applying to non-Hamiltonian systems and indicating the number of constants of motion, but also can be more lightweight and noise-robust than COMET.
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。