PIMCST: Physics-Informed Multi-Phase Consensus and Spatio-Temporal Few-Shot Learning for Traffic Flow Forecasting

TL;DR

This work tackles cross-domain traffic forecasting under scarce data by reframing prediction as a multi-phase consensus problem. It introduces MCPST, a physics-informed framework that fuses diffusion-based propagation, synchronisation of traffic rhythms, and spectral structural analysis through an adaptive consensus and meta-learning for rapid cross-city adaptation. The approach delivers state-of-the-art results across four real-world datasets, with strong gains in few-shot and long-horizon settings, while providing interpretable phase dynamics and reliability estimates. The combination of diffusion, synchronisation, and spectral modules with horizon-specific, uncertainty-aware predictions offers practical benefits for data-scarce urban environments and supports robust, scalable deployment in real-world ITS contexts.

Abstract

Accurate traffic flow prediction remains a fundamental challenge in intelligent transportation systems, particularly in cross-domain, data-scarce scenarios where limited historical data hinders model training and generalisation. The complex spatio-temporal dependencies and nonlinear dynamics of urban mobility networks further complicate few-shot learning across different cities. This paper proposes MCPST, a novel Multi-phase Consensus Spatio-Temporal framework for few-shot traffic forecasting that reconceptualises traffic prediction as a multi-phase consensus learning problem. Our framework introduces three core innovations: (1) a multi-phase engine that models traffic dynamics through diffusion, synchronisation, and spectral embeddings for comprehensive dynamic characterisation; (2) an adaptive consensus mechanism that dynamically fuses phase-specific predictions while enforcing consistency; and (3) a structured meta-learning strategy for rapid adaptation to new cities with minimal data. We establish extensive theoretical guarantees, including representation theorems with bounded approximation errors and generalisation bounds for few-shot adaptation. Through experiments on four real-world datasets, MCPST outperforms fourteen state-of-the-art methods in spatio-temporal graph learning methods, dynamic graph transfer learning methods, prompt-based spatio-temporal prediction methods and cross-domain few-shot settings, improving prediction accuracy while reducing required training data and providing interpretable insights. The implementation code is available at https://github.com/afofanah/MCPST.

Figures (7)

• Figure 1: The proposed MCPST Architecture for few-shot traffic forecasting: ($A_1$) graph-based (GNN) spatio-temporal feature extractions; ($A_2$) multi-phase dynamic modelling through diffusion, synchronisation, and spectral analysis; ($B$) adaptive multi-phase consensus fusion with reliability-aware attention; ($C$) multi-scale spatio-temporal encoding with LSTM-transformer processing; and ($D$) horizon-specific prediction with uncertainty quantification and neural consensus.
• Figure 2: Phase attention weights across different traffic conditions: (a) Rush hours exhibit diffusion phase dominance for congestion modelling during morning/evening peaks; (b) Regular traffic shows synchronisation phase emphasis for coordinated flow management; (c) Unusual events trigger spectral phase spikes for anomaly detection at incident periods.
• Figure 3: Few-shot learning analysis on METR-LA dataset:(a) Adaptive window selection achieves MAE 1.473 (35.9% improvement over random); (b) Meta-learning converges with three stable loss components; (c) Cross-dataset adaptation reaches 90% performance within 15 steps; (d) Consistent outperformed across all datasets versus six baselines.
• Figure 4: Phase dominance analysis and prediction validation: (a) Weekly phase weight evolution showing Diff peaks during rush hours, Sync dominance during steady states, and Spec elevation during weekends; (b) Node-specific predictions across five locations with average MAE 2.198 km/h.
• Figure 5: Spatiotemporal analysis components: (a) Spatial correlation matrix; (b) Traffic flow patterns; (c) Prediction performance across time horizons.

Theorems & Definitions (8)

• Theorem 1: Diffusion Representation
• proof : Proof Sketch
• Theorem 2: Synchronisation Representation
• proof : Proof Sketch
• Theorem 3: Spectral Representation
• proof : Proof Sketch
• Theorem 4: Multi-Phase Consensus Fusion
• proof : Proof Sketch