arXiv:2505.23863cs.LGcs.AI2025-05被引 1

用生成状态空间模型从短观测数据重建混沌系统,精度超基准44%。

PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models

  • 结合Mamba与物理约束,通过时延嵌入重构吸引子流形。
  • 在洛伦兹96系统上预测准确率提升44%,拓扑保真度提高8%。
  • 适合数据稀疏、有噪声的混沌系统研究,如气候与神经科学。

理解混沌动力学是气候科学、神经科学和流体动力学等多个领域的基础问题,但直接实验与干预往往不可行。混沌系统重构旨在从观测时间序列中构建一个保留系统不变几何与长期时间特征的代理动力学模型,从而为系统性扰动与分析提供可控基础。然而,高观测成本常导致数据仅限于短而断续的序列,覆盖时长有限。传统方法如回声状态网络在数据稀缺时表现不佳,因需长时间同步窗口来定位吸引子上的状态;而深度学习时间序列模型虽能拟合局部轨迹,却常丢失全局不变量,导致长期动力学完整性崩溃。本文提出PhyxMamba框架,融合Mamba-based状态空间模型与物理信息原则。通过时延嵌入重建吸引子流形,并采用几何感知正则化的生成训练策略,有效捕捉局部演化与全局物理约束。在模拟与真实混沌系统上的大量实验表明,PhyxMamba在预测精度上优于最强基线44%,在洛伦兹96系统上拓扑保真度提升8%,且对部分观测与噪声具有强鲁棒性。代码已开源:https://github.com/changliu01/PhyxMamba。

原文摘要 · Abstract (English)

Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible. Chaotic system reconstruction aims to identify a surrogate dynamical model that preserves a system's invariant geometric and long-term temporal signatures from observed time series, thereby providing a controllable foundation for probing its mechanisms through systematic perturbation and analysis. However, faithful system reconstruction is hampered by high observational costs, which often restrict data to short, discontinuous sequences spanning only limited timescales. Conventional approaches such as reservoir computing struggle in this data-scarce regime since they typically require long-term synchronization windows to localize states on the attractor. Similarly, while deep learning-based time-series forecasting models effectively fit local trajectories, they often fail to capture global invariants, leading to a collapse of long-term dynamical integrity. Here, we propose PhyxMamba, a framework that synergizes Mamba-based state-space models with physics-informed principles. By leveraging time-delay embeddings to reconstruct the attractor manifold and employing a generative training scheme with geometry-aware regularization, PhyxMamba effectively captures both fine-grained local evolution and global physical constraints. Extensive experiments on simulated and real-world chaotic systems demonstrate that PhyxMamba achieves superior reconstruction performance, outperforming the strongest baseline by over 44% in prediction accuracy and 8% in topological fidelity on the Lorenz96 system, while exhibiting strong robustness against partial observations and noise. Codes are available at https://github.com/changliu01/PhyxMamba.

混沌系统状态空间生成模型时延嵌入

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