学习非正则哈密顿动力学，提升长期模拟稳定性。
Neural non-canonical Hamiltonian dynamics for long-time simulations
- 直接学习向量场或通过数值格式学习离散动力学
- 解决训练后数值不稳定的难题，实现长时间模拟
- 适用于等离子体物理等复杂系统的建模与仿真
本文研究从数据中学习非正则哈密顿动力学，长期预测要求模型和数值方法均保持结构不变。以往研究分别关注模型结构（基于势能架构）或数值方案（退化变分积分器），但二者结合后出现新问题：学习模型可能因方案的规范依赖性导致数值不稳定，使长期模拟失败。本文识别该问题并提出两种训练策略：直接学习向量场，或通过数值格式学习时间离散动力学。多个数值测试验证了方法在学习复杂物理动力学（如回旋等离子体物理中的引导中心动力学）方面的有效性。
原文摘要 · Abstract (English)
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet, respectively with a potential-based architecture and with degenerate variational integrators, but new issues arise when combining both. In experiments, the learnt model is sometimes numerically unstable due to the gauge dependency of the scheme, rendering long-time simulations impossible. In this paper, we identify this problem and propose two different training strategies to address it, either by directly learning the vector field or by learning a time-discrete dynamics through the scheme. Several numerical test cases assess the ability of the methods to learn complex physical dynamics, like the guiding center from gyrokinetic plasma physics.
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