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Inferring Urban Mobility Interactions from Aggregated Dynamics

Yi Wang, Jing Li, Jinliang Deng, Zhenghong Wang, Yizhi Zhang, Fan Zhang, Ivor W. Tsang, Yu Liu

arXiv:2609.07349v1cs.LG

TL;DR

The paper asks whether aggregated inflow and outflow can reveal future origin-destination flows without showing who moves where. It uses those aggregated signals to infer OD flows, and finds stronger reconstruction performance in models that better follow generation-before-assignment logic.

  • Problem

    The question is whether aggregated inflow and outflow, which reveal nothing about who moves where, retain enough information to recover future OD flows.

    Source: Results · p. 3, Discussion · p. 8

  • Method

    ODIN infers fine-grained OD flows from coarse node-level inflow, outflow, and total-flow dynamics.

    Source: Results · p. 3, Discussion · p. 8

  • Results

    Models that better follow generation-before-assignment logic achieve stronger reconstruction performance.

    Source: Discussion · p. 9

  • Takeaways & Limitations

    After training, ODIN draws only on aggregated observations.

    Source: Discussion · p. 8

    Improving robustness under atypical conditions remains an area for future work.

    Source: Discussion · p. 9

Abstract

from arXiv · show

Real-time urban governance depends not only on knowing where people are, but on how they move between places, directional flows that could be conventionally resolved by tracking individuals through space, i.e., expensive to sustain and built on traces that are highly unique and readily re-identifiable. Here we show that this directional structure need not be observed to be known: aggregated counts which cities already collect retain enough information to reconstruct the temporal evolution of origin-destination (OD) matrix. Using an uncertainty-aware physics-informed framework, we infer future OD flows from area-level counts alone across twelve mobility datasets from cities in the United States and China, reaching accuracy comparable to models that take historical OD matrices as input. Probabilistic modeling corrects the systematic underestimation of sparse, high-value corridors and yields calibrated predictions consistent with observed flows. Architectures that respect the generation-before-assignment logic of transport planning recover interactions more faithfully, indicating that location-level spatial heterogeneity should be preserved before pairwise interactions are reconstructed. Because inference requires only aggregated observations after training, recovering interactions this way reduces reliance on continuous individual-level tracking, pointing toward a more deployable and less exposure-heavy basis for real-time urban intelligence.

Results

Across twelve datasets, the Results section evaluates ODIN’s recovery of OD flows from aggregated counts, including its accuracy, probabilistic predictions, and modeling approach. It also examines estimated sensing costs and mobility-record exposure, noting that recovered flows are model estimates rather than collected individual trajectories and that aggregation provides no formal privacy guarantee.

(1) Recovery from aggregated inputs matches OD-based models

  • Across twelve datasets, ODIN matches or exceeds models using complete historical OD matrices and improves RMSE by up to 15% over the strongest aggregated-input competitor.The comparison is reported in Fig. 3a and Extended Data Fig. 1.Source: (1) Recovery from aggregated inputs… · p. 4
  • ODIN preserves observed day-of-week variation and has the smallest weekend fluctuation among compared models.These temporal-structure results are reported in Fig. 3b,c.Source: (1) Recovery from aggregated inputs… · pp. 4–5
  • Time-series and OD-generation methods are less competitive because temporal forecasting lacks explicit OD interactions, while spatial allocation tracks short-term dynamics less effectively.The results indicate that temporal dependencies and spatial interactions must be modeled jointly.Source: (1) Recovery from aggregated inputs… · p. 5
  • Node-level spatiotemporal methods, particularly STAEformer and UQGNN, outperform most baselines, while OD-forecasting methods show no clear advantage in this setting.The findings suggest that effective node-level representations matter: decoding from reconstructed edge features may introduce redundant or noisy interactions.Source: (1) Recovery from aggregated inputs… · p. 5
  • ODIN combines node-level spatiotemporal representation learning with physics-informed TRGM and uncertainty-aware DGMM to constrain edge reconstruction and improve reliability under imbalanced flows.TRGM constrains reconstruction from node-level dynamics; DGMM addresses imbalanced OD-flow distributions.Source: (1) Recovery from aggregated inputs… · p. 5

(2) ODIN holds up where recovery is hardest

  • Prediction error rises with OD-flow magnitude across methods, making sparse, high-value corridors the hardest interactions to infer from aggregated observations.The passage identifies these corridors as operationally important and describes the difficulty as intrinsic to recovery from aggregated observations.Source: (2) ODIN holds up where recovery is… · p. 5

Results across high-value flows, time, and space

  • ODIN errors grow most slowly for rare, high-value flows, form a lower bound across most hours, and yield fewer high-error links with more spatially coherent predictions.The reported advantages extend across high-value flows, temporal variations, and spatial interaction patterns.Source: (2) ODIN holds up where recovery is… · p. 5

Uncertainty improves the recoverable reliability

  • ODIN outperforms uncertainty-aware baselines on CRPS and JSD, while its epistemic uncertainty concentrates on difficult links and can help calibrate high-value flow recovery.Aleatoric uncertainty remains relatively stable, reflecting irreducible randomness in mobility demand; epistemic uncertainty varies with flow magnitude and prediction error and is associated with imbalanced observations.Source: (3) Uncertainty improves the… · pp. 5–6

Aggregated dynamics retain sufficient information for interaction inference

  • Even with only one total-flow count per location, ODIN recovers OD structure at accuracy close to full OD observations, while static allocation and gravity baselines perform far worse.Accuracy degrades only marginally as inputs progress from historical OD matrices to node-level inflow/outflow and then total flow; node-first methods remain stable, unlike edge-first methods including ODMixer.Source: Aggregated dynamics retain sufficient… · p. 6

Generation-before-assignment logic explains the advantage of node-first modeling

  • The node-first ODIN outperforms an edge-first variant in most input settings, and access to historical OD matrices only partly narrows the gap.The authors attribute the gap partly to early pairwise construction introducing redundant interactions, whereas node-first modeling preserves compact, informative representations before OD inference.Source: Generation-before-assignment logic… · p. 7
  • Node-first modeling yields smoother latent structure and clearer spatial clustering, supporting the principle that representing places before flows produces more faithful recovery.Edge-first features separate more by forecast horizon, while node-first features group nodes with similar flow levels more coherently; this aligns with the generation-before-assignment logic of mobility.Source: Generation-before-assignment logic… · p. 7

Reducing data acquisition burden and privacy exposure

  • Recovering OD interactions from aggregated dynamics reduces dependence on trajectory-level data acquisition and exposure.The section introduces an annualized cost analysis using literature-calibrated unit prices, but the supplied passages do not include its cost results.Source: Reducing data acquisition burden and… · p. 7

Results

  • Across datasets, area-level aggregated sensing costs US$4.85–9.38 million versus US$18.38–257.37 million for trajectory acquisition, a 73.6–96.4% annual burden reduction.The lower trajectory-cost estimate uses a US$25 volunteer GPS-survey incentive and is described as highly conservative; real-world trajectory data collection would likely cost more.Source: Reducing data acquisition burden and… · pp. 7–8
  • OD flows had 43.9% unique-cell rate (k=1) and 61.8% low-3 exposure (k=3); inflow/outflow aggregation lowered these to 16.3% and 24.0%, reductions of 72.0% and 67.9%.Source: Reducing data acquisition burden and… · p. 8
  • Total-flow aggregation further reduced average unique-cell rate and low-3 exposure to 12.1% and 18.2%, respectively.Source: Reducing data acquisition burden and… · p. 8
  • These exposure reductions provide no formal privacy guarantee; ODIN infers flows from aggregate counts without collecting or holding individual trajectories at inference.The reduction in exposure therefore arises at the sensing stage, not merely from the choice of output.Source: Reducing data acquisition burden and… · p. 8

Discussion

The discussion argues that cities can recover directional mobility interactions from aggregate observations rather than continuously tracking individuals. It highlights the modeling order that supports recovery while noting limits in training requirements, sparse or volatile settings, and geographic generalization.

Discussion

  • Aggregated observations that cities already collect can support recovery of fine-grained directional interactions without continuous individual-trajectory collection or full OD matrices.After training, ODIN uses aggregate counts; recovered flows are model estimates rather than records tied to identifiable individuals.Source: Discussion · pp. 8–9
  • Inferred OD dynamics could support epidemic screening, traffic control, event evacuation, and public-transport operations that require directional mobility information.The discussion names transmission corridors and targeted screening, road-segment or corridor signal control, and anticipating demand concentrations.Source: Discussion · p. 8
  • The paper reframes dynamic OD prediction as recovering latent interactions from a coarser aggregate signal, using physical priors and uncertainty modeling to constrain plausible allocations and address sparse, high-value flows.The reframing contrasts this task with forecasting from same-granularity history.Source: Discussion · p. 8
  • Models following transportation planning’s generation-before-assignment order achieve stronger reconstruction by preserving location-level dynamics and spatial heterogeneity before inferring pairwise interactions.The discussion identifies place representation as central to learning locations’ mobility potential.Source: Discussion · p. 9
  • The privacy benefit concerns reduced acquisition and retention of individual-level records, not a formal anonymity or differential-privacy guarantee.Aggregated observations may still be susceptible to reconstruction under some conditions.Source: Discussion · p. 9
  • OD-free inference applies at deployment, because training still requires ground-truth OD; accuracy is also limited when sparse, volatile aggregates weakly constrain directional flows.The paper presents the latter as a property of the task rather than of a particular model.Source: Discussion · p. 9
  • Although the datasets span the United States and China, broader cross-regional generalization remains untested, and non-sensitive contextual data may improve robustness under atypical conditions.Examples proposed include road networks, land use, weather, events, and transit schedules.Source: Discussion · p. 9

Methodology

The methodology presents ODIN, which maps aggregated node-level inflow and outflow dynamics into representations, models temporal and spatial dependencies, and reconstructs temporally resolved OD interactions. It produces probabilistic future-flow predictions with uncertainty-aware calibration and is evaluated on twelve mobility datasets from cities in the United States and China.

Node-level dynamics embedding

  • ODIN’s node embeddings combine inflow and outflow signals with learnable temporal and adaptive embeddings to represent mobility rhythms and latent spatial heterogeneity.Inflow reflects attraction intensity, while outflow reflects production intensity.Source: Node-level dynamics embedding · p. 10

Spatiotemporal dependencies modeling

  • Transformer blocks first model dependencies across historical time steps and then across spatial units, producing node representations for edge reconstruction.Temporal attention captures fluctuations and periodic changes; spatial attention captures coordinated variations among urban units.Source: Spatiotemporal dependencies modeling · p. 10

Spatiotemporal interaction reconstruction

  • Because aggregated inflows and outflows underdetermine OD matrices, ODIN uses a Temporally Resolved Gravity Model to constrain edge reconstruction.It combines local origin–destination attraction with patch-level temporal compatibility and a geographical distance-decay kernel.Source: Spatiotemporal interaction… · pp. 10–11

Uncertainty-aware spatiotemporal interaction decoding

  • The Disentangled Gaussian Mixture Model predicts OD-flow distributions and separates epistemic from aleatoric uncertainty for reliability-aware calibration.It uses Jensen–Rényi Divergence to estimate epistemic uncertainty from the gap between mixture uncertainty and the average uncertainty of its Gaussian components.Source: Uncertainty-aware spatiotemporal… · p. 12
  • ODIN uses epistemic uncertainty to adaptively compensate the GMM mean, addressing biased estimates of sparse, high-value flows.A compensation branch adds a mean term, while a gating-weighted function controls the compensation strength.Source: Uncertainty-aware spatiotemporal… · pp. 12–13

Loss functions and training process

  • ODIN combines likelihood, expected-flow supervision, and mixture-entropy regularization, with exponential moving averages used to smooth parameter updates.The likelihood fits observed flows, L1 regularization supervises predicted magnitude, and entropy regularization encourages components to capture different flow regimes.Source: Loss functions and training process · pp. 13–14

Datasets and evaluation setup

  • Evaluation spans twelve datasets: taxi and bike-sharing records from New York City and Chicago, and anonymized mobile-phone records from four Chinese cities.U.S. trips were aggregated by taxi zones or community areas; Chinese records were aggregated by subdistricts.Source: Loss functions and training process · p. 14
  • The U.S. datasets use 1-hour intervals and the China datasets 2-hour intervals, with 8,784 and 4,392 snapshots, respectively, covering 2024.Source: Loss functions and training process · p. 14

Aggregated dynamics

Filtering and evaluation settings

  • Filtering removes redundant units; core units exceed regional mean hourly flow, while ordinary units have average hourly total flow above one.The evaluation uses a core-region setting of high-volume units and an ordinary-region setting of all non-redundant units.Source: Loss functions and training process · pp. 14–15

Training and evaluation protocol

Figures and tables

Across the reported datasets, ODIN performs strongly using aggregated mobility dynamics, while its uncertainty-aware predictions better preserve difficult OD flows. The figures also compare node-first with edge-first modeling and contrast aggregated sensing with individual-level acquisition.

Figures and tables

  • Adding time-dependent weights to the gravity formulation lets OD interactions vary across temporal states rather than follow one static interaction pattern.The temporal extension reduces errors, particularly for high-flow OD regimes.Source: Figures and tables · p. 19
  • ODIN combines a spatiotemporal Transformer with gravity-informed and uncertainty-learning modules to infer OD flows from aggregated inputs.Its components include a Temporal Resolved Gravity Model and a Disentangled Gaussian Mixture Model.Source: Figure 2 · p. 19, Figures and tables · p. 20
  • Across cities, transport modes, and spatial settings, ODIN achieves consistently strong or top/near-top performance using aggregated mobility dynamics as input.The reported tables cover RMSE, MAE, and WAPE.Source: Figures and tables · pp. 20, 24
  • ODIN produces fewer high-error links and more spatially coherent errors, while its error rises more slowly for sparse, high-value flows.It also maintains lower errors across daily demand periods, and its epistemic uncertainty better aligns with difficult OD links.Source: Figure 4 · p. 21, Figures and tables · p. 21
  • Node-first modeling achieves lower RMSE, MAE, and WAPE than edge-first modeling across OD, inflow/outflow, and total-flow inputs.Its latent representations are smoother and more compact, with clearer temporal organization and stronger separation by flow magnitude.Source: Figure 5 · p. 22, Figures and tables · p. 22
  • Area-level aggregated sensing reduces exposure to unique or low-count mobility records and requires lower annual acquisition costs than trajectory-level acquisition.The comparison covers taxi and bike-sharing datasets.Source: Figure 6 · p. 23, Figures and tables · p. 23
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