CoSynFlow：用于耗散哈密顿动力学跨系统预测的保形辛神经流

中文摘要 AI 辅助

学习微分方程的解算子是科学机器学习的核心问题，但许多神经算子方法仅优化预测精度，未显式遵循动力学的几何结构。SympNets和辛神经流等保结构模型通过保持辛形式解决了保守哈密顿系统的该问题，而具有保形辛结构的耗散哈密顿系统中，辛形式会按耗散决定的保形因子演化。本文提出CoSynFlow，一种用于学习耗散哈密顿动力学连续时间解映射的保形辛神经流，它将辛剪切映射与显式保形缩放结合，通过构造保持保形辛结构；通过对有限维哈密顿描述符和耗散参数进行条件设置，单个训练好的模型无需重新训练即可预测未见系统的解映射。CoSynFlow的结构误差保持在机器精度，达到最低的长时预测误差，并支持物理信息训练。

英文摘要

Learning solution operators for differential equations is a central problem in scientific machine learning. However, many neural operator methods optimize prediction accuracy without explicitly enforcing the geometric structure of the dynamics. Structure-preserving models such as SympNets and Symplectic Neural Flows address this issue for conservative Hamiltonian systems by preserving the symplectic form. In dissipative Hamiltonian systems with conformal symplectic structure, however, the symplectic form evolves according to a conformal factor determined by the dissipation. We propose CoSynFlow, a conformal symplectic neural flow for learning continuous-time solution maps of dissipative Hamiltonian dynamics. CoSynFlow composes symplectic shear maps with explicit conformal scaling, preserving the conformal symplectic structure by construction. By conditioning it on a finite-dimensional Hamiltonian descriptor and the dissipation parameter, a single trained model predicts solution maps for unseen systems without retraining. CoSynFlow keeps the structure error at machine precision, attains the lowest long-horizon error, and admits physics-informed training.

发表机构

• RIKEN AIP（理化学研究所先进智能项目）
• IMI, Kyushu University（九州大学信息医学研究所）

机构由 AI 辅助整理，请以论文原文为准。