# Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems

arXiv: https://arxiv.org/abs/2608.29057 · HTML: https://mlsanity.com/paper/2608.29057/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [LpWM: A Case for Sparse Representations in World Models](https://mlsanity.com/paper/2608.22764/) (2026)
- [On the lifting and reconstruction of nonlinear systems with multiple invariant sets](https://mlsanity.com/paper/2304.11860/) (2023)
- [Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits](https://mlsanity.com/paper/1911.11996/) (2019)
- [Course Correcting Koopman Representations](https://mlsanity.com/paper/2310.15386/) (2023)
- [Properties of Immersions for Systems with Multiple Limit Sets with Implications to Learning Koopman Embeddings](https://mlsanity.com/paper/2312.17045/) (2023)

## Abstract (arXiv)

Koopman autoencoders (KAEs) seek a higher-dimensional latent representation in which nonlinear dynamics evolve linearly. However, many interesting systems have multiple basins of attraction, and both theoretical and empirical work has shown these multibasin systems cannot generally admit a single finite-dimensional global Koopman embedding under standard assumptions. We posit that encoders with a sparsity-inducing objective encouraging few active latent coefficients will provide latent supports as an inspectable basin-modeling principle for Koopman autoencoders. We use these encoders producing sparse latents in training Sparse Koopman Autoencoders (SKAEs) without basin labels or other regime annotations, and treat the learned latent supports as model-produced regime variables after training. Across a range of procedurally generated multibasin systems and chaotic flows, we show that SKAEs have superior forecasting performance compared to dense-latent KAEs. We also perform a mechanistic study that shows latent supports produced by SKAEs are both essential for the quality of the representation and useful for identifying basins on basin-interior states, whereas dense-latent KAEs collapse to an uninformative single support family. These results identify sparse latents and their corresponding supports as label-free, interpretable regime variables for Koopman learning in nonlinear systems with multiple local dynamical laws.