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Mamba Integrated with Physics Principles Masters Long-term Chaotic System Forecasting
Created by
Haebom
Author
Chang Liu, Bohao Zhao, Jingtao Ding, Huandong Wang, Yong Li
Outline
This paper addresses the fundamental yet underexplored challenge of long-term prediction of chaotic systems from short-term observations. Existing approaches either rely on long-term training data or focus on short-term sequence correlations, which struggle to maintain prediction stability and dynamical consistency over long periods of time. In this paper, we propose PhyxMamba, a novel framework that captures the underlying dynamics of chaotic systems by integrating Mamba-based state-space models and physical information principles. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate predictions. Mamba replicates physical processes through generative training schemes, and enhances prediction accuracy by enforcing physical constraints through multi-token predictions and attractor geometric regularization, preserving key statistical invariants. Extensive evaluations on a variety of simulated and real chaotic systems demonstrate that PhyxMamba provides excellent long-term predictions from short-term data and faithfully captures essential dynamical invariants. This framework opens a new way to reliably predict chaotic systems under conditions of observational data scarcity, providing Takeaways for a wide range of fields including climate science, neuroscience, and epidemiology. The source code is publicly available at https://github.com/tsinghua-fib-lab/PhyxMamba .
