Mamba Integrated with Physics Principles Masters Long-term Chaotic System Forecasting

TL;DR

PhyxMamba is a novel framework combining a Mamba-based state-space model with physics-informed principles to improve long-term forecasting of chaotic systems from limited short-term data.

Contribution

It introduces a physics-informed, Mamba-based approach with attractor reconstruction and regularization for enhanced long-term chaotic system prediction.

Findings

Outperforms existing methods in forecasting accuracy.

Successfully captures key statistical properties of chaotic systems.

Effective on both simulated and real-world data.

Abstract

Long-term forecasting of chaotic systems remains a fundamental challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Conventional approaches, such as reservoir computing, typically require training data that incorporates long-term continuous dynamical behavior to comprehensively capture system dynamics. While advanced deep sequence models can capture transient dynamics within the training data, they often struggle to maintain predictive stability and dynamical coherence over extended horizons. Here, we propose PhyxMamba, a framework that integrates a Mamba-based state-space model with physics-informed principles to forecast long-term behavior of chaotic systems given short-term historical observations on their state evolution. We first reconstruct the attractor manifold with time-delay embeddings to extract global dynamical features. After that, we introduce a generative training scheme that enables Mamba to replicate the physical process. It is further augmented by multi-patch prediction and attractor geometry regularization for physical constraints, enhancing predictive accuracy and preserving key statistical properties of systems. Extensive experiments on simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior forecasting accuracy and faithfully captures essential statistics from short-term historical observations.