Dynamic Multi-period Experts for Online Time Series Forecasting

Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose Dynamic TMoE, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4% and MAE by 7.8%. Code is available at https://github.com/andone-07/Dynamic-TMoE.

Online anomaly detection (OAD) plays a pivotal role in real-time analytics and decision-making for evolving data streams. However, existing methods often rely on costly retraining and rigid decision boundaries, limiting their ability to adapt both effectively and efficiently to concept drift in dynamic environments. To address these challenges, we propose DyMETER, a dynamic concept adaptation framework for OAD that unifies on-the-fly parameter shifting and dynamic thresholding within a single online paradigm. DyMETER first learns a static detector on historical data to capture recurring central concepts, and then transitions to a dynamic mode to adapt to new concepts as drift occurs. Specifically, DyMETER employs a novel dynamic concept adaptation mechanism that leverages a hypernetwork to generate instance-aware parameter shifts for the static detector, thereby enabling efficient and effective adaptation without retraining or fine-tuning. To achieve robust and interpretable adaptation, DyMETER introduces a lightweight evolution controller to estimate instance-level concept uncertainty for adaptive updates. Further, DyMETER employs a dynamic threshold optimization module to adaptively recalibrates the decision boundary by maintaining a candidate window of uncertain samples, which ensures continuous alignment with evolving concepts. Extensive experiments demonstrate that DyMETER significantly outperforms existing OAD approaches across a wide spectrum of application scenarios.

Accurate prediction of nonstationary multivariate time series remains a critical challenge in complex industrial systems such as iron ore sintering. In practice, pronounced concept drift compounded by significant label verification latency rapidly degrades the performance of offline-trained models. Existing methods based on static architectures or passive update strategies struggle to simultaneously extract multi-scale spatiotemporal features and overcome the stability-plasticity dilemma without immediate supervision. To address these limitations, a Drift-Aware Multi-Scale Dynamic Learning (DA-MSDL) framework is proposed to maintain robust multi-output predictive performance via online adaptive mechanisms on nonstationary data streams. The framework employs a multi-scale bi-branch convolutional network as its backbone to disentangle local fluctuations from long-term trends, thereby enhancing representational capacity for complex dynamic patterns. To circumvent the label latency bottleneck, DA-MSDL leverages Maximum Mean Discrepancy (MMD) for unsupervised drift detection. By quantifying online statistical deviations in feature distributions, DA-MSDL proactively triggers model adaptation prior to inference. Furthermore, a drift-severity-guided hierarchical fine-tuning strategy is developed. Supported by prioritized experience replay from a dynamic memory queue, this approach achieves rapid distribution alignment while effectively mitigating catastrophic forgetting. Long-horizon experiments on real-world industrial sintering data and a public benchmark dataset demonstrate that DA-MSDL consistently outperforms representative baselines under severe concept drift. Exhibiting strong cross-domain generalization and predictive stability, the proposed framework provides an effective online dynamic learning paradigm for quality monitoring in nonstationary environments.