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Zero-shot forecasting of chaotic systems
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Evaluates zero-shot time-series foundation model Chronos on forecasting 135 chaotic systems against custom-trained baselines, finding competitive short-term accuracy, good attractor reconstruction for large models, and context-parroting as a mechanism.
Problem
Whether zero-shot time-series foundation models can forecast chaotic dynamical systems, which are outside their training domain, in both short-term accuracy and long-term attractor statistics.
Approach
Benchmarks pre-trained Chronos models zero-shot on the dysts suite of 135 chaotic systems against per-system custom-trained baselines, evaluating short-term valid prediction time and attractor geometry, and probes the mechanism via context shuffling and overlap analysis.
Key results
- Across 135 chaotic systems, the three largest zero-shot Chronos models have statistically indistinguishable median VPT and outperform all baselines except N-BEATS (Friedman test, p<1e-3).
- Zero-shot Chronos forecasts remain accurate up to about 1 Lyapunov time, with performance increasing monotonically with context length up to 512 points (over 17 Lyapunov times).
- Large zero-shot models capture attractor fractal dimension well; a fully trained small Transformer matches zero-shot attractor reconstruction despite weaker point forecasts.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase Chronos model size | Chronos zero-shot forecasting · dysts benchmark | VPT | Helped |
| Increase Chronos model size | Chronos zero-shot forecasting · dysts benchmark | attractor reconstruction accuracy | Helped |
| Use Chronos-8M or Chronos-20M instead of one of the three largest Chronos models | Chronos zero-shot forecasting · dysts benchmark | VPT | Hurt |
| Increase context length (ablation) | Chronos-base zero-shot forecasting · dysts benchmark | VPT | Helped |
| Shuffle length-k sequences while retaining the final k context points (ablation) | Chronos zero-shot forecasting · dysts benchmark | forecast accuracy | Mixed |
| Make the trajectory more nonstationary with exponential modulation (ablation) | Chronos-base zero-shot forecasting · dysts benchmark | VPT | Hurt |
| Fine-tune Chronos-base on chaotic-system trajectories | Chronos-base · Held-out chaotic-system trajectories | forecast accuracy | No clear effect |
| Fine-tune Chronos-base on chaotic-system trajectories | Chronos-base · Datasets randomly drawn from Chronos's training corpus | forecast accuracy | Hurt |
| Use full-state multivariate forecasts instead of channel-independent forecasts (ablation) | Baseline models · dysts benchmark | VPT | Helped |
| Use full-state multivariate forecasts instead of channel-independent forecasts (ablation) | Baseline models · dysts benchmark | sMAPE | Helped |
Surprising findings
- Chronos forecasts remain accurate for a while even when context is shuffled at k-gram level, indicating that statistical distribution information rather than exact order drives in-context learning.
- Fine-tuning Chronos-base on the chaotic dataset did not improve validation scores and slightly degraded performance on its original training distribution.
Limitations
- Chronos is univariate, so each coordinate is forecast independently, losing cross-dimension information.
- Performance is sensitive to initial condition and degrades under nonstationarity/distribution shift.
- Fine-tuning Chronos on chaotic data was unsuccessful at the scale tried.
Experimental setup
Datasets: dysts chaotic systems benchmark (135 systems) real double pendulum video dataset
Benchmarks: dysts
Metrics: sMAPE valid prediction time (VPT) correlation dimension error KL divergence between attractors
Baselines: N-BEATS TiDE NVAR LSTM Transformer Chronos-base fine-tuned
Builds on: Chronos N-BEATS TiDE dysts benchmark
Closest papers by meaning
- A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems (NeurIPS 2026 · similarity 0.89)
- TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting (NeurIPS 2026 · similarity 0.88)
- TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning (NeurIPS 2025 · similarity 0.87)
- True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics (NeurIPS 2025 · similarity 0.87)
- Zero-shot Imputation with Foundation Inference Models for Dynamical Systems (ICLR 2025 · similarity 0.87)
- Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective (NeurIPS 2024 · similarity 0.87)
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