Network-Wide Freeway Speed Nowcasting and Forecasting from Sparse Fixed Sensors with a Probe-Supervised Graph Convolutional Recurrent Network

Ran Tu; Zihao Li; Arash Mirzaei

cs.LGOct 15, 2026

Network-Wide Freeway Speed Nowcasting and Forecasting from Sparse Fixed Sensors with a Probe-Supervised Graph Convolutional Recurrent Network

Authors: Ran Tu, Zihao Li, Arash Mirzaei

Organizations: North Central Texas Council of Governments, Arlington, TX 76011, USA

Abstract

Traffic agencies need current and near-future speeds on every link of their network, but their fixed sensors cover only part of it. We study joint nowcasting and next-hour forecasting of hourly speeds on all 4{,}127 directional freeway links of the Dallas--Fort Worth region from sensors on 643 links (15.6%). Historical probe-vehicle data supervise every link in training; only sensor readings are used at inference. We call this setting probe-supervised sparse sensing. We propose GCRN+, a graph convolutional recurrent network that predicts deviations from a historical speed profile. It combines a parameter-free, direction-aware kernel interpolation of sensor anomalies, used as input features and as an output baseline, with a diffusion-convolutional GRU on the directed road graph, a low-rank adaptive graph and learnable link embeddings. It scales linearly with network size and trains on a CPU. Sensor readings are emulated from probe speeds, which isolates spatio-temporal inference from detector calibration. On four held-out test days, GCRN+ attains an RMSE of 2.21~~mph for the current hour and 2.39~~mph for the next hour on unsensored links, against 3.23~~mph for the historical average. The best baselines that use the same interpolation features reach 2.53 and 2.75~~mph. Adapted recent models without these features (STID, STAEformer, ImputeFormer, MoGERNN) reach at best 2.54 and 2.53~mph; this comparison is between complete pipelines rather than architectures. GCRN+ is best in every distance band except links not connected to any sensor through the road graph. Ablations within one recurrent backbone attribute most of the gain to the link embeddings and the adaptive graph, which can be trained because probe labels exist for every link. For congestion detection on unsensored links, recall rises from 77% (historical average) and 86% (best competitor) to 89% at aprecision of 0.94.

Figures & tables

Figure 1: DFW freeway network (4,127 directional TMC links). Orange: links with a fixed sensor. Blue shades: network distance from an unsensored link to the nearest sensor (upstream or downstream). Grey: links not connected to any sensor through the directed road graph. Counts are numbers of links.

Panel of Figure 2 — Figure 2: GCRN+ architecture. Sensor anomalies are first spread over the network by a parameter-free, direction-aware masked kernel interpolation, which provides both input features and an output baseline. A two-layer diffusion-convolutional GRU then operates on three graph supports: the downstream and upstream transition matrices of the road graph and a learned low-rank adaptive graph. A learnable link embedding is part of the input at every step. The head predicts corrections to the baseline for the current and the next hour.

Figure 3: RMSE on unsensored links versus network distance to the nearest sensor (seed 42). The last group (unreachable) is categorical. Dashed: baselines without learning. Road-graph models are accurate near sensors; embedding-based models (AGCRN, STAEformer) are better far from them. GCRN+ is best in every group except the unreachable links.

	Now ( $t$ )			Next hour ( $t{+}1$ )
Model	100% (643)	50% (322)	25% (161)	100% (643)	50% (322)	25% (161)
HA	3.23	3.26	3.26	3.23	3.26	3.26
HA + interpolation	2.93	3.01	3.10	3.18	3.24	3.25
GBDT (interp. features)	2.54	2.60	2.70	2.80	2.80	2.82
GCRN	2.53	2.61	2.72	2.74	2.78	2.83
ImputeFormer	2.62	2.72	2.76	2.69	2.79	2.86

Table 5: Sensitivity to sensor density: RMSE (mph) on links without a sensor when only a random subset of the 643 sensor links is kept (number of sensors in parentheses). Models are retrained for each density (seed 42). Removed sensor links join the evaluation set, so the set of evaluated links differs slightly between columns.

Figure 4: Network travel time index on the four test days (current hour). Top: probe ground truth. Bottom: estimation error when unsensored links use the historical average, HA + interpolation, or GCRN+.

Figure 5: Time–space diagram of I-30 eastbound on October 31, 2024 (current-hour estimates). Left: probe speeds. Middle and right: absolute error of HA + interpolation and of GCRN+. Orange ticks mark sensor links. Hours 0–1 (incomplete input window) and 23 (no next-hour target within the day) are not estimated and are left blank.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Shared training settings
Input window / horizon	3 hours / current + next hour
Optimiser	Adam, learning rate $2\times 10^{-3}$ (STAEformer $10^{-3}$ ), halved after 2 stagnant epochs
Batch, epochs, early stopping	8 windows, $\leq 40$ epochs, patience 6 on validation RMSE
Sensor dropout	fraction $U(0,0.4)$ of sensors hidden per sample
Loss	Huber ( $\delta=1$ ) on standardised anomalies; observed current cells weight 0.1
Gradient clipping	5

Appendix

Table 7: Hyperparameters. All deep models share the training settings in the first block.

Model	Parameters	Epochs	Train (min)	Inference (s/day)
Ridge (interp. features)	–	–	1	–
GBDT (interp. features)	–	–	3	–
GRU (no graph)	13,730	40	28	0.7
DCRNN	55,586	40	94	3.1
GCRN	62,114	40	94	3.3
AGCRN	252,536	40	82	2.5

Appendix

Table 8: Model size and cost on a 10-core CPU. Training minutes are averaged over seeds and were measured with three to four jobs running in parallel; they are only comparable relative to each other. Inference: seconds to produce one full test day (21 network-wide predictions).

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GAS-PFN: Graph-Aware Spatiotemporal Prior-Data Fitted Networks for Zero-Shot Traffic Forecasting

Joseph Natter, Long Vu, Yifan Zhang, Bobin Deng+2

Kennesaw State University · Missouri State University

Traffic Forecasting Spatiotemporal Forecasting Zero-Shot Time Series Forecasting Prior-Data Fitted Networks Spatiotemporal Transformers

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Traffic forecasting requires modeling complex temporal dynamics and the spatial dependencies imposed by road topology. Supervised graph-based models achieve strong performance, but are often trained for a particular dataset and sensor graph, making deployment to new or evolving networks costly. Prior-Data Fitted Networks (PFNs) offer a zero-shot alternative by learning in-context inference from synthetic task priors, which provide an explicit mechanism for encoding domain-specific assumptions. Existing forecasting PFNs, however, do not explicitly represent the graph-structured dependencies governing traffic dynamics. To combine graph-aware traffic modeling with zero-shot adaptation, we introduce the Graph-Aware Spatiotemporal Prior-Data Fitted Network (GAS-PFN). GAS-PFN incorporates sampled road topology into its synthetic task prior through random-walk diffusion, teaching the model to learn graph-coupled dynamics during pretraining. Its co-designed inference architecture uses two mask-conditioned passes through a shared Transformer backbone to separately model sensor-specific temporal dynamics and spatiotemporal interactions among neighboring sensors before integrating their representations for prediction. This design enables GAS-PFN to use target-network structure and context without parameter updates. Across six benchmarks at the 90-minute horizon, GAS-PFN reduces MSE by 34.0% on average relative to TimePFN, its closest PFN-based predecessor. It also reduces MSE by 27.7% on average relative to four recent industry-developed general-purpose zero-shot forecasters. In this comparison, all models receive 90 minutes of contiguous recent history, and any additional context is drawn from each dataset's chronological training split. These results indicate that aligning PFN priors and inference architectures with graph structure improves in-context learning for zero-shot traffic forecasting.

Abstract

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