Problem
Research questions and friction points this paper is trying to address.
distribution dynamics
unpaired snapshots
infinite-dimensional distribution space
dynamical learning
Koopman representation
DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
🤖 AI Summary
This study addresses the challenge of learning complex system dynamics from unpaired distributional snapshots, where conventional methods struggle with the infinite dimensionality of distribution spaces. To overcome this limitation, this work proposes treating distributions directly as dynamical states and performing modeling within the distribution space. By extending deep Koopman operator theory to distributional dynamics, a unified framework is constructed to jointly learn predictive observables, finite-dimensional representations, and generative mappings, thereby effectively circumventing the infinite-dimensional bottleneck. The proposed approach achieves state-of-the-art extrapolation performance across seven benchmarks and substantially mitigates error accumulation in long-horizon predictions, establishing a novel paradigm for modeling distributional evolution in complex systems.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Deep Koopman Learning
Distribution Dynamics
Unpaired Snapshots
Generative Map
Long-horizon Prediction
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