Sundial is a family of generative time series foundation models. This version is pre-trained on 1 trillion time points with 128M parameters. For more information, please refer to this paper. [Slides] [Poster] [Intro (CN)].

The model can make zero-shot predictions for point and probabilistic forecasting. Not only the mean or quantiles, you can get any statistical predictions with a set of generated samples.

Sundial can be viewed as an ARMA model (Auto-Regression and Moving-Average). Transformer learns auto-regressive token representations. Conditioned on them, TimeFlow transforms random noises into non-deterministic predictions.

Overall Architecture: The input time series is divided into patch tokens, which are embedded from the original continuous values. The patch embeddings are fed into a decoder-only Transformer, a stable and speedup version that learns token representations. The model is optimized using our TimeFlow Loss, a parameterized loss function that models per-token probability distribution conditioned on the learned representations, and generates multiple plausible predictions under the flow-matching framework.

Quickstart

pip install transformers==4.40.1 # Use this version and Python 3.10 for stable compatibility

python

import torch
from transformers import AutoModelForCausalLM

# load pretrain model
# supports different lookback/forecast lengths
model = AutoModelForCausalLM.from_pretrained('thuml/sundial-base-128m', trust_remote_code=True) 

# prepare input
batch_size, lookback_length = 1, 2880 
seqs = torch.randn(batch_size, lookback_length)

# Note that Sundial can generate multiple probable predictions
forecast_length = 96 
num_samples = 20

output = model.generate(seqs, max_new_tokens=forecast_length, num_samples=num_samples)

# use raw predictions for mean/quantiles/confidence-interval estimation
print(output.shape) 

More examples for predicting quantiles or confidence intervals are provided in this notebook.

Evaluation

We evaluate performance on the following benchmarks:

We are actively working around it and are glad to hear suggestions and noteworthy cases :)

Inference Time

Hardware: Apple M1 Pro CPU (16 GB)

Lookback Length	Prediction Length	# Generated Samples	Inference Time	Accelerate By
672	16	1	249ms	-
2880	16	1	510ms	FlashAttention
2880	720	1	510ms	Multi-Patch Prediction
2880	1440	1	789ms	KV Cache
2880	720	20	949ms	Shared Condition

Hardware: A100-40G GPU, following Chronos paper.

Specification

Architecture: Causal Transformer (Decoder-only)
Pre-training Scale: 1032B time points
Context Length: up to 2880
ReNorm: Default=True
Patch Length: 16
Multi-Patch Prediction Length: 720
Parameter Count: 128M
Number of Layers: 12
Precision: FP32
Speedup: KV Cache & FlashAttention

Acknowledgments

This work was supported by the National Natural Science Foundation of China (62022050 and U2342217), the BNRist Innovation Fund (BNR2024RC01010), and the National Engineering Research Center for Big Data Software.

The model is mostly built from the Internet public time series dataset, which comes from different research teams and providers. We sincerely thank all individuals and organizations who have contributed the data. Without their generous sharing, this model would not have existed.

Citation

If you find Sundial helpful for your research, please cite our paper:

@article{liu2025sundial,
  title={Sundial: A Family of Highly Capable Time Series Foundation Models},
  author={Liu, Yong and Qin, Guo and Shi, Zhiyuan and Chen, Zhi and Yang, Caiyin and Huang, Xiangdong and Wang, Jianmin and Long, Mingsheng},
  journal={arXiv preprint arXiv:2502.00816},
  year={2025}
}

Contact

If you have any questions or want to use the code, feel free to contact:

Yong Liu (liuyong21@mails.tsinghua.edu.cn)
Guo Qin (qinguo24@mails.tsinghua.edu.cn)

License

This model is licensed under the Apache-2.0 License.