Koopman Operator Identification of Model Parameter Trajectories for Temporal Domain Generalization (KOMET)

Temporal Domain Generalization (TDG) has emerged to address real-world streaming data with distribution shifts over time. However, existing methods are either prone to overfitting to domain-specific noise in the data space or become overly complex and less interpretable in the parameter space. To bridge these gaps, we propose AdaSpecK, a spectral-Koopman framework with adaptive context extraction for TDG. To mitigate noise fitting to irregularly sampled domains, we introduce spectral-regularized Koopman dynamics modeling, which applies spectral-aware filtering in the latent space to extract denoised low-frequency trajectories and learn a Koopman operator to model the system dynamics in a linearized space. To model complex historical environments under non-stationarity, we design a context-informed heterogeneous pattern extraction mechanism. Specifically, we employ a target-conditioned attention module to attend to distinct past windows, producing a dynamic, target-specific historical summary. By constructing an environmental signature from the current evolutionary pattern, our model adaptively perceives which aspects of the past context are most informative for future prediction via a learned router. Extensive experiments on eight diverse classification and regression benchmarks demonstrate that AdaSpecK achieves state-of-the-art performance. The code and datasets are available at \href{}{https://anonymous.4open.science/r/Ada-Spec-K}.

Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients. We introduce two complementary components that make Koopman predictors more robust. First, we add an attention-free latent memory (AFT) block that aggregates a short window of past latents to produce a corrected latent before each Koopman update. Unlike multi-head attention, AFT operates in linear time and adds only $\approx$30k parameters ($3d^2 + T^2$, fewer than matched multi-head attention), yet captures the local temporal context needed to suppress error divergence. Second, we propose dynamic re-encoding: lightweight, online change-point triggers (EWMA, CUSUM, and sequential two-sample tests) that detect latent drift and project predictions back onto the autoencoder manifold. Across three benchmark systems -- Duffing oscillator, Repressilator, IRMA -- our model consistently reduces error accumulation compared to a Koopman autoencoder and matched-capacity multi-head attention. We also compare against GRU and Transformer autoencoders, evaluated both from initial conditions and with a 50-step context, and find that Koopman+AFT (with optional re-encoding) attains markedly lower long-horizon error while maintaining lower inference latency. We report improvements over horizons up to 1000 steps, together with ablations over trigger policies. The result is a fast, compact predictor that stays on the learned manifold over long horizons.

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/