True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics (2505.13192v1)

Abstract: Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Overview of "True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics"

The paper "True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics" by Christoph Jürgen Hemmer and Daniel Durstewitz presents a notable advancement in the field of dynamical systems reconstruction (DSR). The authors introduce DynaMix, a novel architecture leveraging a mixture-of-experts model based on Almost-Linear Recurrent Neural Networks (AL-RNNs), which is pre-trained to generalize zero-shot to out-of-domain dynamical systems (DS). This research addresses a significant deficiency in existing models, which lack the ability to perform zero-shot inference and often falter in maintaining the long-term statistical properties of dynamical systems.

Key Contributions

1. Zero-Shot Dynamical Systems Reconstruction: DynaMix stands out as the first architecture capable of zero-shot DSR. It successfully reconstructs previously unseen dynamical systems while preserving their long-term statistical characteristics. This is a critical step forward, as existing time series models like Chronos often fail on out-of-domain systems and do not adequately capture long-term dynamics.
2. Architecture and Efficiency: The mixture-of-experts model is composed of AL-RNNs and features multivariate information transfer, making it highly effective in capturing the dependencies among various state dimensions of a dynamical system. Furthermore, the model is computationally efficient, achieving high performance with a relatively lightweight architecture compared to TS foundation models, enabling orders of magnitude faster inference times.
3. Comparison with Time Series Foundation Models: The paper rigorously compares DynaMix with existing TS foundation models, such as Chronos-t5 and Mamba4Cast, demonstrating superior performance across established measures. In particular, DynaMix outperforms these models in terms of geometrical and long-term temporal agreement, as measured by $D_{\text{stsp}$ and $D_H$, respectively. Moreover, DynaMix often matches or exceeds these models in short-term forecasting accuracy, showcasing its robustness.

Methodological Insights

DynaMix's architecture is optimized for DSR by utilizing a multivariate mixture-of-experts framework that can efficiently generalize across diverse DS. The training leverages sparse teacher forcing, allowing the model to explore future trajectories while managing gradient stability, crucial for handling chaotic systems. This method ensures the long-term statistical properties of the target systems are accurately replicated.

Implications and Future Directions

The implications of this work are manifold. Practically, DynaMix provides a more reliable tool for forecasting systems in fields such as climate science, neuroscience, and economics, where understanding long-term dynamics is crucial. Theoretically, it offers insights into architectural features and training methodologies conducive to zero-shot inference capabilities.

Looking ahead, the paradigm adopted by DynaMix could stimulate further integration of dynamical systems theory into time series forecasting models. Future research may explore expanding the model architecture to include a wider range of empirical data types in its training process, potentially enhancing the generalization capabilities further. Additionally, addressing the challenges posed by non-stationary or multi-scale dynamics could fortify DynaMix's applicability in real-world scenarios.

Overall, this paper provides a significant contribution to the armamentarium for dynamical systems analysis, setting a new benchmark in zero-shot DSR with potential implications that extend beyond the immediate scope.