u/DangerousFunny1371

In our #NeurIPS2026 paper “A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems (DS)” (preprint: https://arxiv.org/abs/2607.14937) we reduce a DS foundation model to the ingredients minimally necessary to faithfully reproduce long-term statistical and geometrical properties of DS:

A piecewise affine map with only a single (!!) parameter α that controls local con-/divergence rates, and …
… a context selector that chooses from the provided context signal the data point closest to the current state of the map, thus ensuring the generated dynamics stays close to the context in its temporal and geometrical properties.

With just these two mechanisms, this minimal form – which we coined DynaBase – can reproduce all major dynamical regimes, including fixed points (α<1), limit cycles (α=1), and chaotic attractors (α>1). Thus, unlike other simple mechanisms like context parroting, DynaBase even preserves the correct dynamical regime!

Surprisingly, it turns out that this simple context-driven 1-parameter map outperforms most major time series and DS foundation models, as well as custom-trained models, in both long-term statistics and even short-term predictions, even when run in zero-shot mode.

Both inference and training are extremely cheap – training can be done either analytically in one step by linear regression on forward-predictions, or by 1-parameter grid search directly on DS reconstruction objectives → this reveals interesting performance differences induced by different training mechanisms.

Most importantly in our minds, DynaBase owing to its formal simplicity may thus provide a tractable mathematical handle on analyzing, improving & understanding the performance and training of some time series and DS foundation models.

https://preview.redd.it/jmlcnocq5gth1.png?width=3000&format=png&auto=webp&s=1fc322e17a77575ddb0be3525482b45c70fa28f1

In our #ICML2026 position paper we argue a dynamical systems perspective is needed to drive time series (TS) modeling forward: https://arxiv.org/abs/2602.16864

Essentially all time series in nature and engineering come from some underlying dynamical system (DS), mostly chaotic for complex systems, and acknowledging this helps to address many open problems.

Dynamical systems reconstruction (DSR) goes beyond mere forecasting and gives us an understanding of the dynamical rules that underlie observed time series. This in turn may enable true out-of-domain generalization and predicting a system’s long-term behavior, something current TS models cannot do. In the paper, we compare a variety of custom-trained and recent foundation models for TS and DSR w.r.t. short- & long-term forecasting.

Specifically, we suggest:

Put a focus on DSR-specific training techniques and objectives in TS model training, such as generalized teacher forcing (https://proceedings.mlr.press/v202/hess23a.html). These will enable capturing long-term statistical properties and dynamical structure, and at the same time help massively reducing parameter load and complexity of TS models. Proper training is more important than model architecture!
Pretrain TS models on simulations from dynamical systems, rather than on artificially created time series functions. These will yield much more natural priors for real-world TS. Chaotic systems in particular contain a rich temporal structure and many timescales (often an infinite skeleton of unstable periodic orbits of any period).
Move away from transformers, back to modern RNNs. DS are defined by recursions in time. By ignoring this and potentially further coarse-graining signals, transformers lose essential dynamical information, making them generally incapable of capturing a system’s dynamical rules. This is evidenced by their failure to forecast a DS’ long-term statistical or geometrical structure.
Address the hard problems in TS modeling: Topological shifts (https://proceedings.mlr.press/v235/goring24a.html). Although in itself tricky, the really hard problem in TS forecasting is not so much mere out-of-distribution shifts, but changes that drive a system across tipping points or into different dynamical regimes, where the vector field topology changes.
DS properties like attractors or bifurcations are universal – acknowledging this in TS modeling will give a kind of mechanistic and transferable understanding of TS properties that is independent from specific (physical, medical, …) domain knowledge. It therefore also pays off to put a focus on mathematically tractable and interpretable models.

With a great team of shared-first & co-authors, Christoph Hemmer, Charlotte Doll, Lukas Eisenmann & Florian Hess!

A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems [R]

Time Series Modeling Needs a Dynamical Systems Perspective [R]