TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching

Accurate prediction of multivariate time series is essential for emerging network intelligent control, observability, and management functions. Existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time series. They prioritize improvements in average prediction accuracy, while overlooking heterogeneous dependency structures and performance variability across individual time series. Recent advances in large language models have introduced new directions for multivariate time series forecasting; however, their application in conjunction with explicit structural dependency modeling remains relatively underexplored, especially in networked environments. In this paper, we present a topology-aware learning framework for large-scale network traffic prediction that explicitly models both temporal dynamics and structural dependencies in multivariate network time series. We first investigate a graph attention model designed to capture topology-induced correlations among network traffic time series. We then evaluate a fine-tuned large language model-based representations for improved generalization across heterogeneous traffic patterns. To further address the diversity of cross-correlations in high-dimensional traffic data, we introduce a clustering-based preprocessing stage that groups traffic flows with similar dependency characteristics prior to model training, reducing input complexity and improving learning stability. Experiments on real backbone traffic data show consistent improvements over statistical and recurrent neural network baselines. In addition to average accuracy, we evaluate performance across individual time series and observe reduced variability in prediction quality.

City-wide traffic forecasting is important for congestion management, route guidance, and intelligent transportation systems, but accurate prediction remains challenging when future traffic must be generated as spatial maps over an entire urban network. Existing traffic movie prediction methods have improved frame-level accuracy, yet many still treat forecasting mainly as image reconstruction. This can produce traffic maps that are numerically close to the ground truth but weakly constrained by road layout, connectivity, travel direction, and congestion propagation, especially in cross-city settings where both traffic behavior and road structure change. To address this limitation, this study proposes RCSNet, a road-conditioned spatiotemporal network that reformulates traffic movie prediction as topology-guided future-state generation. RCSNet extracts road-aware representations from static road maps, models multi-horizon traffic dynamics from historical observations, aligns directional traffic features with local road structure, and progressively generates future traffic maps for improved temporal consistency. A structure-consistent learning objective further encourages predictions to remain accurate, road-aligned, and spatially stable. Experiments across multiple cities show that RCSNet improves both forecasting accuracy and structural consistency. In same-city forecasting on Berlin, Antwerp, and Moscow, RCSNet reduces average MAE, MSE, and RMSE by 11.5%, 10.0%, and 5.1%, respectively, compared with the closest baseline. In cross-city testing on unseen Chicago and Bangkok, it reduces RMSE by 10.6% and 10.5% without target-city fine-tuning. Additional horizon-wise, road-structure, explainability, statistical, and efficiency analyses show that RCSNet produces more accurate, transferable, road-aligned, and computationally efficient traffic forecasts.

We study the task of learning the structure of a $d$-sparse Gaussian graphical model on $n$ variables from a single trajectory of Glauber dynamics. Beyond algorithmic considerations, many applications present temporally correlated observations rather than i.i.d.\ samples. In the classical i.i.d.\ setting, under comparably general sparsity and minimum edge-strength assumptions, sublinear-in-$n$ sample guarantees are known, but achieving them in polynomial-time remains open. Motivated in part by this gap, we give a polynomial-time algorithm that recovers the conditional-independence graph from a single Glauber trajectory, with a trajectory-length guarantee that does not depend on the mixing time. Technically, our algorithm has three components. First, we estimate the conditional variances and rescale the trajectory to reduce to the unit-diagonal case, without changing the underlying graph. Second, we design a local edge test that extracts adjacency information from short update windows by isolating pairwise influence. Third, we aggregate these local statistics using a robust median-based estimator, and prove accuracy despite temporal dependence arising from a single trajectory.