ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908801458765824 |
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| author | Liu, Chang Zhao, Bohao Ding, Jingtao Li, Yong |
| author_facet | Liu, Chang Zhao, Bohao Ding, Jingtao Li, Yong |
| contents | Foundation models have shown 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. Codes are available at https://github.com/TomXaxaxa/ChaosNexus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness Liu, Chang Zhao, Bohao Ding, Jingtao Li, Yong Machine Learning Artificial Intelligence Foundation models have shown 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. Codes are available at https://github.com/TomXaxaxa/ChaosNexus. |
| title | ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2509.21802 |