DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
Abstract
Many complex systems are observed only through temporally unpaired distribution snapshots, making trajectory-based dynamical learning difficult without additional assumptions. We therefore formulate the problem directly in distribution space, treating the distribution itself as the dynamical state. The challenge is that distribution space is infinite-dimensional, making compact and approximately closed representations difficult to learn from finite snapshots. We introduce DisKO, which extends deep Koopman learning to distribution dynamics by jointly learning predictive distributional observables, a finite-dimensional Koopman representation, and a generative map back to the full distribution. Across seven diverse benchmarks, DisKO achieves state-of-the-art extrapolation performance, with substantially slower error accumulation on long-horizon prediction tasks. DisKO further recovers leading Koopman eigenvalues and eigenfunctions on systems with analytic spectra, revealing meaningful dynamical structure in the learned representation.
Related
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- Reconstruction-Aware Distribution Matching for Inverse Problems with Unpaired Data
- Learning from Totally Unpaired Data via Minimum Conditional Entropy Coupling
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BibTeX
@misc{ma2026disko,
title = {{DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots}},
author = {He Ma and Xiaochen Liu and Wanfeng Lu and Ying Wang and Wei Lin and Qunxi Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34629},
eprint = {2609.34629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34629},
}
RIS
TY - UNPB
TI - DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
AU - He Ma
AU - Xiaochen Liu
AU - Wanfeng Lu
AU - Ying Wang
AU - Wei Lin
AU - Qunxi Zhu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34629
UR - https://arxiv.org/abs/2609.34629
AB - Many complex systems are observed only through temporally unpaired distribution snapshots, making trajectory-based dynamical learning difficult without additional assumptions. We therefore formulate the problem directly in distribution space, treating the distribution itself as the dynamical state. The challenge is that distribution space is infinite-dimensional, making compact and approximately closed representations difficult to learn from finite snapshots. We introduce DisKO, which extends deep Koopman learning to distribution dynamics by jointly learning predictive distributional observables, a finite-dimensional Koopman representation, and a generative map back to the full distribution. Across seven diverse benchmarks, DisKO achieves state-of-the-art extrapolation performance, with substantially slower error accumulation on long-horizon prediction tasks. DisKO further recovers leading Koopman eigenvalues and eigenfunctions on systems with analytic spectra, revealing meaningful dynamical structure in the learned representation.
ER -