aiqbench analysis
DisKO advances deep Koopman learning by operating directly in distribution space, enabling accurate long-horizon predictions from unpaired snapshots without relying on trajectory assumptions. The method successfully recovers meaningful dynamical structures like eigenvalues and eigenfunctions while demonstrating superior extrapolation performance across diverse benchmarks. This represents a significant theoretical and practical step forward for modeling complex systems where traditional state-space representations are insufficient.
DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
arXiv:2609.34629v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Dynamical Systems (math.DS)
arXiv:2609.34629 [cs.LG]
(or arXiv:2609.34629v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.34629 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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