ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness

Foundation models show great promise in achieving zero-shot or few-shot forecasting for ODE-based chaotic systems via large-scale pretraining. However, existing architectures often fail to capture the multi-scale temporal structures and distinct spectral characteristics of chaotic dynamics. To address this, we introduce ChaosNexus, a foundation model for chaotic system forecasting underpinned by the proposed ScaleFormer architecture. By processing temporal contexts across hierarchically varying patch sizes, ChaosNexus effectively captures long-range dependencies and preserves high-frequency fluctuations. To address heterogeneity across distinct systems, we integrate Mixture-of-Experts (MoE) layers into each ScaleFormer block and explicitly condition the final forecasts on a learned frequency fingerprint, providing the model with a global spectral view of the system. Extensive evaluations on over 9,000 synthetic systems demonstrate that ChaosNexus achieves superior fidelity in long-term attractor statistics while maintaining competitive point-wise accuracy. Furthermore, in real-world applications, it achieves a remarkable zero-shot mean error below 1°C for 5-day station-based weather forecasting. Code is available at https://github.com/tsinghua-fib-lab/ChaosNexus.

Many important natural systems, including weather, fluid motion, and biological signals, change in ways that are difficult to predict: a tiny difference now can lead to very different outcomes later. This makes it hard for AI models to learn reliable forecasting rules from limited observations. We introduce ChaosNexus, an AI model that learns from a large collection of simulated examples of complex changing systems and applies this knowledge to new systems. The model examines the past at multiple time scales, allowing it to capture both fast changes and slower, broader patterns. It also learns to recognize the characteristic dynamics of each system, which helps it adapt its forecasts to different kinds of behavior. Tests on thousands of simulated systems show that ChaosNexus achieves strong forecasting accuracy while more faithfully preserving the long-term behavior of these systems. It also works well on real-world weather station data, achieving strong five-day temperature forecasts even without weather-specific training. These results suggest that AI models trained on diverse simulated systems can provide useful forecasting knowledge for real scientific problems.