Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems
Abstract
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.
Related
- Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
- A prism hierarchy of learning regimes in large linear autoencoders
- A Data-Driven Koopman-Behavioral Distance for Nonlinear Dynamical Systems
- Forced-Term Modeling in the Koopman Framework for Linear Operator Learning in Nonlinear Dynamical Systems
- Koopman Observability of Nonlinear Systems and Data-Driven Koopman--Luenberger Observer
BibTeX
@misc{li2026sparse,
title = {{Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems}},
author = {Aidan Li and Uday Kiran Reddy Tadipatri and Mahan Fathi and Sarath Chandar and Ross Goroshin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.29057},
eprint = {2608.29057},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29057},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems
AU - Aidan Li
AU - Uday Kiran Reddy Tadipatri
AU - Mahan Fathi
AU - Sarath Chandar
AU - Ross Goroshin
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.29057
UR - https://arxiv.org/abs/2608.29057
AB - 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.
ER -