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

Abstract

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.