Title: KIND: Blending Stationary and Transient Koopman Dynamics with Learned Uncertainty
Primary area: learning on time series and dynamical systems
Keywords: Koopman operator, operator learning, hybrid models, time series forecasting, uncertainty-aware prediction, dynamical systems, scientific machine learning

Abstract: We introduce KIND, a hybrid forecasting architecture that produces uncertainty-aware predictions by blending stationary and transient dynamics through Koopman operators. Classical system identification relies on fixed models of predictable behavior, while modern neural forecasting often sacrifices structure for flexibility. KIND operates at their intersection: it decomposes time series into components governed by stationary (model-driven) and transient (attention-driven) dynamics. These components are modeled independently via Koopman operators acting on lifted embeddings and fused through a Kalman-inspired, uncertainty-weighted blending mechanism. Crucially, KIND learns to estimate its own predictive confidence, enabling it to identify unfamiliar dynamics, adapt its forecasts, and express when its outputs can be trusted. A physics-informed pretraining strategy further strengthens its stationary pathway, encouraging robust separation of dynamic modes. Across both real-world and benchmark datasets - including superconducting radio frequency cavity measurements and electricity load forecasting - KIND demonstrates competitive accuracy, interpretable uncertainty, and resilience to distributional shifts, outperforming classical methods like Online DMD and competing neural models such as Koopa.

TL;DR: KIND leverages Koopman operators and uncertainty-weighted blending to forecast nonstationary time series with interpretable confidence scores.