Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how to predict the behavior of systems that change over time, even when the system moves into completely new conditions not seen during training. They identify why previous models struggled to make such predictions, mainly because the models made incorrect assumptions about how real-world systems work. To fix this, the authors propose new methods, including splitting features differently, and provide a mathematical way to know how far predictions can be trusted. Their experiments show that these improvements help models make accurate forecasts in new, unseen scenarios like tipping points without needing extra training.
dynamical systemsout-of-domain predictionzero-shot learningtipping pointsfeature splittinglatent featuresmodel extrapolationhyper-networkstime series forecasting
Authors
Georg Trede, Charlotte Ricarda Doll, Elias Weber, Daniel Durstewitz
Abstract
Predicting the behavior of dynamical systems (DS) beyond the dynamical and parameter regimes observed in training is a pivotal and essentially unresolved problem in scientific ML. It is central to any good scientific theory, which we expect to be able to make predictions about regimes not covered by currently available data. Recent hierarchical and hyper-network guided approaches for DS reconstruction (DSR) enable training on many DS simultaneously, and revealed that extracted latent features are often related to crucial control parameters of the underlying DS that varied across the training corpus. However, true out-of-domain forecasting abilities of these models, e.g., across tipping points, remain limited, and fine-tuning, or even full model retraining, on time series from the new dynamical regime is usually required. Here, we mathematically analyze the root of these limitations in previous model formulations and identify three core shortcomings rooted in a mismatch between structural assumptions of the reconstruction model and typical properties of physical systems. We propose a combination of remedies for these shortcomings, most importantly feature splitting, and furthermore derive a closed-form bound on the reliable extrapolation range. We demonstrate empirically that our techniques allow for accurate zero-shot prediction into new dynamical regimes, outside the observed training regime, as, e.g., encountered across tipping points.