Deep learning predicts complex system changes from few snapshots
DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
Machine Learning
Summary
Many systems change over time but we only get to see scattered snapshots of how they look. This makes it hard to understand how they evolve because we don’t see smooth timelines. The authors created DisKO, a method that looks at these snapshots as whole distributions instead of individual steps, and learns patterns to predict future changes more accurately. DisKO does this by turning complex data into simpler mathematical forms and then turning those back into full pictures, helping it predict far ahead with less error.
What this means in practice
- •For environmental modelers: Predict distribution changes in complex environmental data from irregular observations for better long-term forecasts.
- •For manufacturing system engineers: Improve prediction of system state changes from limited discrete measurements for enhanced process control.
Authors
He Ma, Xiaochen Liu, Wanfeng Lu, Ying Wang, Wei Lin, Qunxi Zhu
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.