ChaosNexus

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

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://anonymous.4open.science/r/ChaosNexus-C809.

Our Model

Installation

Environment

• Tested OS: Linux
• Python 3.11.0
• PyTorch 2.8.0

Dataset

Obtain the released major dataset from [Hugging Face], and the Weather-5K dataset from [OneDrive]. Then place the downloaded data in the folder./data.

Pre-trained Models

If you require the pre-trained parameters of ChaosNexus for reproduction or fine-tuning, please download them from [Dropbox].

Experiment Reproduction

1. Major Dataset Experiments

To reproduce the results on the major dataset, please follow the instructions below for different models.

Training

ChaosNexus

1. Open ./scaleformer/scaleformer/scaleformer.py and set the variable MODEL_NAME to 'Nexus'.
2. Run the training script:

bash ./scripts/scaleformer/run_predict_finetune-Nexus.sh

Panda (Baseline)

1. Open ./scaleformer/scaleformer/scaleformer.py and set the variable MODEL_NAME to 'Panda'.
2. Run the training script:

bash ./scripts/scaleformer/run_predict_finetune-Panda.sh

Chronos (Fine-tuning)

1. Download the public pre-trained weights.
2. Run the fine-tuning script:

bash ./scripts/chronos/run_finetune.sh

Evaluation

After training is complete, evaluate the models using:

bash ./scripts/scaleformer/run_eval.sh

or evaluate Chronos-SFT using:

bash ./scripts/chronos/run_eval.sh

2. Weather Dataset Experiments

For the Weather-5K dataset, additional preprocessing and specific evaluation steps are required.

Preprocessing After downloading the data to ./data, convert the format using:

python ./scripts/transform_weather.py

Fine-tuning Configuration Before starting the fine-tuning process, you must modify the model initialization logic. Please open ./scripts/train.py, locate the Initialize model section, comment out the currently active code block, and uncomment the alternative block specifically for fine-tuning.

Inference Run the prediction script. Crucially, you must ensure the following flags are set to true to generate the necessary output files for benchmarking:

# Ensure these arguments are included in your run command
eval.save_labels=true \
eval.save_predictions=true \
eval.save_contexts=true

3. Baseline Models Reproduction

To reproduce the results of other baseline models (control group) used for comparison in our paper, we utilize the Time-Series-Library.

Please refer to the official repository: thuml/Time-Series-Library for the implementation of these advanced deep time series models. We follow the standard training and evaluation protocols provided in their library to ensure a fair comparison.

Benchmarking Once the predictions are generated, run the benchmark script to obtain the final results:

python ./scripts/benchmark_weather.py

License

The software in this repository is freely available under MIT license. Please see the license for further details.