# Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction

arXiv: https://arxiv.org/abs/2606.22969 · HTML: https://mlsanity.com/paper/2606.22969/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 72 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Continual learning with hypernetworks](https://mlsanity.com/paper/1906.00695/) (2019)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/2201.08910/) (2022)
- [A State Space Approach for Piecewise-Linear Recurrent Neural Networks for Reconstructing Nonlinear Dynamics from Neural Measurements](https://mlsanity.com/paper/1612.07846/) (2016)
- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control](https://mlsanity.com/paper/2009.04278/) (2020)
- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Homotopy-based training of NeuralODEs for accurate dynamics discovery](https://mlsanity.com/paper/2210.01407/) (2022)
- [Interpretable Meta-Learning of Physical Systems](https://mlsanity.com/paper/2312.00477/) (2023)
- [Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning](https://mlsanity.com/paper/2312.06283/) (2023)
- [Meta-Dynamical State Space Models for Integrative Neural Data Analysis](https://mlsanity.com/paper/2410.05454/) (2024)

## Abstract (arXiv)

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.