MobilityGen: Deep Generative Mobility Model

• MobilityGen is a deep generative modeling framework that simulates realistic human mobility trajectories by integrating behavioral attributes and built environment context.
• It employs a transformer-based denoising diffusion probabilistic model to generate mobility sequences that align with empirical laws like Zipf's law and radius of gyration.
• The framework facilitates urban planning and public health analysis by simulating social exposure, access disparity, and disease spread with high contextual accuracy.

MobilityGen is a deep generative modeling framework for the simulation of realistic human mobility trajectories, primarily at daily or multi-day scales and over large geographic extents. The approach is distinguished by its explicit integration of multiple behavioral attributes—such as location, temporal scheduling, activity duration, and travel mode selection—with built environment context (e.g., POI distributions, urban spatial geometry). MobilityGen uses a transformer-based denoising diffusion probabilistic model (DDPM) to achieve a flexible, dynamic, and context-aware generative process. Its outputs accurately capture empirically observed regularities in human movement—such as scaling laws for visited location frequencies and radius of gyration evolution—while supporting the analysis of complex phenomena like urban access disparity and social exposure.

1. Model Architecture and Generative Methodology

MobilityGen models individual mobility as a chronological sequence of activity events, where each event is defined by a tuple: (location, start time, duration, travel mode). These are embedded as follows:

• Categorical variables (location IDs, travel modes) are represented via learnable embeddings (lookup tables).
• Continuous variables (start time, duration) are fed through dedicated feed-forward modules before combination.

Environmental context, such as the coordinates of locations and attributes extracted via POI-based representations, is processed and integrated with behavioral embeddings using residual connections.

The core generative engine is a denoising diffusion probabilistic model (DDPM): a Markov chain gradually corrupts the latent encoding $z_0$ of the entire mobility sequence into Gaussian noise over $T$ discrete steps ($$q(z_1,\ldots,z_T|z_0) = \prod_{t=1}^T q(z_t|z_{t-1})$$). A transformer-based encoder processes the observed (traveled) sequence, yielding features that guide the reverse diffusion process (denoising). The decoder reconstructs an approximation $\hat{z}_0$, which is then decoded into event tuples via linear task-specific heads.

The reconstruction loss for training is

$$\mathcal{L}_{\text{reconstruct}} = \mathbb{E}\left[ \left\| \hat{h}(z_t, t) - z_0 \right\|^2 \right]$$

where $\hat{h}$ is the network’s estimator of the denoised latent code $z_0$ from noisy $z_t$.

2. Incorporation of Behavioral and Environmental Attributes

A fundamental advance in MobilityGen is the concurrent modeling of multiple behavioral and environmental dimensions:

• Location, start time, duration, and travel mode are encoded in a shared latent space, ensuring their joint influence over subsequent steps in a trajectory.
• Spatial context is represented both as raw coordinates (transformed using methods such as Space2vec) and as functional POI-based attributes (often using Latent Dirichlet Allocation or similar topic models).
• These factors are fused through residual connections prior to passage through the transformer, ensuring that the generative process conditions on both individual behavior and environmental constraints.

This setup enables the model to learn context-conditioned preferences (e.g., travel mode selection given POI density, or time allocation in relation to spatial features).

3. Empirical Regularities and Validation

MobilityGen is explicitly validated against a range of empirical “laws” from mobility science:

• Scaling law for visited locations: Zipfian behavior in rank-frequency of locations is recovered, as is the logarithmic growth of the individual’s radius of gyration with step number, computed as

$$r_u(k) = \sqrt{ \frac{1}{k} \sum_{i=1}^k (l^{(i)} - l_u^{(cm)})^2 }$$

where $l^{(i)}$ is the $i$-th visited location and $l_u^{(cm)}$ is the center of mass.

• Temporal mobility entropy: The entropy and predictability of a user’s schedule (capturing daily routines and exploratory habits) are accurately matched between simulated and empirical samples.
• Travel mode and activity coupling: The coupled evolution of travel mode and destination choice is maintained, reproducing dependencies evident in real-world data.

Model outputs are quantitatively compared to GNSS-based traces, as well as to baselines including the EPR model, Container model, and Markov-chain-based approaches. Performance comparisons use likelihood ratio tests, Wasserstein distances, and motif frequency distributions, with MobilityGen demonstrating close alignment to empirical distributions.

4. Latent Space Structure and Behavioral Insights

The latent embedding space learned by MobilityGen facilitates both interpretability and advanced behavioral analysis:

• Mode clustering: Embeddings projected (e.g., via densMAP) reveal distinct clusters for similar travel modes.
• Temporal unfolding: Time and duration manifest as smooth manifolds, supporting the detection of behavioral trajectories and anomalies.
• Correlation with external factors: Embeddings can be examined for association with socioeconomic indicators or urban infrastructure, enabling further analysis of mobility determinants.

A notable insight is the model's ability to diagnose access disparities across travel modes. For example, it finds that car and walking modes are tightly aligned with primary urban anchors, while bus and tram modes display greater deviation. This suggests a nuanced understanding of sustainable mobility and access equity unattainable with earlier models.

5. Simulation of Social and Urban Dynamics

MobilityGen’s event-centric, context-aware approach enables simulation of higher-order phenomena:

• Co-presence and exposure: By generating individualized activity schedules, the model can estimate the overlap (co-presence) between individuals of different income segments, thereby reconstructing experienced segregation or social mixing.
• Urban access analysis: Simulations elucidate patterns in spatial accessibility, e.g., how the urban form and mode infrastructure jointly affect individual activity spaces over time.
• Scenario assessment: By altering environmental conditions or behavioral priors, the model enables counterfactual analysis (e.g., evaluating changes in segregation or access under modified infrastructure).

These outputs are critical for data-driven studies in public health (epidemic modeling), urban planning, and transportation equity.

6. Applications, Limitations, and Future Directions

MobilityGen’s capacity to generate synthetic but realistic activity sequences supports applications in:

• Urban planning: Informing land-use and transportation policies by providing counterfactual scenario analysis under varying infrastructure or regulation.
• Public health: Modeling disease spread by quantifying fine-grained interpersonal contact rates and exposure networks.
• Data privacy: Generating synthetic datasets for research and policy evaluation without the sensitivity of raw GNSS traces.

Potential areas for future work include the integration of finer-grained environmental and social contextual cues (e.g., weather, real-time events, socio-demographics), refinement of spatial discretization for enhanced resolution, and hybridization with agent-based/utility-driven decision models to further increase interpretability and policy relevance. A plausible implication is the broad adoption of such models for generative data augmentation, simulation-based evaluation of proposed interventions, and explainable mobility analytics.

7. Summary Table: Core Components of MobilityGen

Component	Function	Mathematical Principle
DDPM backbone	Sequence generation	Markov Gaussian noise process
Transformer encoder/decoder	Latent event representation	Self-attention, residual connections
Behavioral attribute fusion	Joint modeling of event features	Embedding, feedforward mapping
Environmental context	Conditioning on space/POI	Space2vec, POI-based LDA
Validation regime	Empirical pattern recovery	Zipf’s law, radius of gyration

MobilityGen, through its DDPM-transformer architecture, provides a flexible, scalable, and context-enabled simulation platform for mobility sequence generation, with robust empirical validation and a demonstrated capacity to yield new analytical perspectives on mobility-driven phenomena (Hong et al., 7 Oct 2025).