Koopman Generative Operators for Efficient Probabilistic Time-Series Forecasting

TL;DR

Koopman Generative Operators (KGO) enable fast, accurate probabilistic time-series forecasting by modeling uncertainty evolution in a Koopman latent space. It combines Koopman Patch Embedding, Koopman Flow Matching for single-step generation via matrix exponentials, and an Adaptive Uncertainty Gate for per-variable, per-horizon uncertainty adaptation. KGO achieves state-of-the-art performance on most ProbTS benchmarks with over 25× faster inference than iterative methods.

Why It Matters

KGO bridges the gap between accuracy and efficiency in probabilistic forecasting, making high-quality uncertainty quantification practical for real-time applications like finance, energy, and logistics. Its single-step generation eliminates the bottleneck of iterative sampling, enabling deployment in latency-sensitive systems without sacrificing predictive fidelity.

Key Findings

• KGO achieves state-of-the-art results on 13/17 benchmarks in CRPS and 16/17 in NMAE.
• Koopman Flow Matching enables single-step generation via closed-form matrix exponentials, reducing inference time by at least 25×.
• The Adaptive Uncertainty Gate learns variable- and horizon-specific aleatoric uncertainty without manual tuning.