Simultaneous inference of environmental and interaction forces in collective dynamics

Collective dynamics arise in a wide range of physical, biological, and engineering applications. Examples include cell migration, swarm robotics, social dynamics, and animal behavior. A defining characteristic of these systems is the emergence of large-scale coordination from local interactions among agents; a fundamental question is thus to understand the local interactions that give rise to the observed emergent dynamics. We are interested in methods for learning interactions generally, which can describe a wide class of physical systems exhibiting collective dynamics defined by an interaction kernel, without a priori assumptions on the analytical form of this kernel (i.e. it is nonparametric). The advantage of this kernel-based approach is that it incorporates the underlying physics of the model (i.e. collective dynamics), which more general equation-learning approaches may ignore, potentially limiting their effectiveness for model accuracy and predictions. In this work, we extend existing variational learning approaches to collective systems with both interaction kernels and environmental/intra-agent forces. The proposed framework simultaneously infers the interaction kernel non-parametrically while learning the environmental force using either semi-parametric or fully nonparametric representations. The methodology is validated on several benchmark models exhibiting synchronization, alignment, attraction-repulsion, and external environmental forces. We also introduce a model-selection procedure based on our nonparametric learning framework to identify models that optimally explain a given set of trajectory observations. By exploiting the feature-identification capability of the learned models, the proposed procedure can distinguish among different collective dynamics frameworks and recover mechanistic interaction mechanisms directly from trajectory data.

Secrets Everywhere: Auditing Memorization in Mobility Prediction Models

Human mobility prediction models, which forecast the next location in a user's trajectory, are increasingly deployed in urban analytics, navigation, and personalized services. Yet, little is known about their potential to memorize and expose sensitive user trajectories from training data. While memorization has been extensively studied in language models, mobility prediction poses unique challenges: training sequences encode human behavior at various spatial and temporal scales, creating privacy risks at different granularities. In this paper, we conduct the first systematic audit of memorization in mobility prediction models. While prior work has shown that privacy leaks can arise from such models, we systematically assess and quantify memorization risks at scale. We identify key challenges, including the lack of a randomness space, the multi-scale structure of trajectories, and user-specific behavioral diversity. To address these challenges, we introduce a framework to quantify mobility memorization at different levels of granularity: individual locations, anchor pairs, and subtrajectory segments. We also develop user-grounded reference sets to assess how likely a model is to prefer training data over realistic alternatives. Our evaluation across multiple models and datasets reveals pervasive memorization patterns that correlate with user regularity and increase the risk of data extraction at inference time. Our findings call for mandatory privacy auditing in mobility prediction models.

Beyond Lanes: Traffic Flow Dynamics in Disordered Conditions Based on High-Resolution Trajectory Data

Disordered traffic flow is characterized by weak or non-existent lane discipline in the presence of strong vehicle heterogeneity and continuous lateral interactions, challenging traditional lane-based modeling assumptions. This study presents an empirical study of macroscopic and microscopic aspects of disordered traffic using high-resolution UAV trajectory data collected on an urban arterial. A two-dimensional extension of Edie's framework is applied to quantify aggregate traffic variables and produce a two-dimensional fundamental diagram, revealing that traffic states cannot be adequately represented using one-dimensional formulations and highlighting the persistent role of lateral redistribution. The propagation of congestion is estimated directly from the spatiotemporal speed fields, demonstrating the emergence of coherent stop-and-go waves and showing a similar dynamics as conventional lane-based flow, in spite of the heterogeneous vehicle interactions. At the microscopic level, steady-state follower-leader identification is used to examine desired time gaps and minimum lateral spacing, vehicle dimension distributions, and kinematic characteristics, revealing pronounced inter-class heterogeneity that explains disordered traffic behavior. The study provides an empirical framework linking vehicle-level interactions and aggregate traffic dynamics and establishes a data-driven basis for the calibration and validation of traffic models for disordered mixed traffic systems.

Staypoint Detection from Noisy Trajectory Data [Experiment Paper]

Detecting staypoints from raw trajectory data is fundamental to numerous spatial computing applications. This process transforms raw numeric sequences of geolocations into semantically meaningful locations, such as homes, workplaces, or restaurants. Despite its importance for semantic trajectory analysis, staypoint detection lacks standard benchmarks, and existing algorithms have never been systematically evaluated. This gap persists because no publicly available datasets provide both raw individual trajectories and ground-truth staypoint annotations. This benchmark paper addresses this limitation with two key contributions: (1) we introduce 16 large-scale simulated datasets capturing thousands of agents with annotated staypoints across varying trajectory noise levels, and (2) we evaluate nine staypoint detection algorithms-including both state-of-the-art and novel methods-to analyze their robustness to noise. Our evaluation reveals that existing state-of-the-art algorithms perform poorly under realistic noise conditions. Conversely, our proposed unsupervised methods yield substantial improvements, while supervised approaches drastically outperform existing baselines. While these results are very promising, these datasets and methods are only meant as starting points for future research in staypoint detection.

Towards Inclusive Mobility Modeling: Characterizing and Evaluating Elderly Trajectory Patterns in Urban Systems

The rapid advance of smart cities increasingly depends on trajectory data mining, yet underrepresented demographic groups, particularly the elderly, are often sparsely represented in public mobility datasets. This underrepresentation can introduce systematic bias into mobility modeling and downstream urban planning. Using the 2016-2020 Jersey City subset of the Citi Bike System Data, this study quantitatively examines how the absence of underrepresented subgroups' mobility signatures affects mobility modeling, using synthetic trajectory generation as a case study. The analysis reveals that elderly riders exhibit a structurally distinct mobility signature, including localized activity spaces (958 m vs. 1,189 m for young riders), lower mobility entropy (1.82 vs. 4.15), and asymmetric off-peak temporal patterns. To demonstrate that relying on majority-dominated training data yields biased synthetic outcomes, we further evaluate both a first-order Markov chain and a Qwen3-4B model fine-tuned with QLoRA across three demographic training settings: the full population, young riders only, and elderly riders only. Results show that models trained on majority-dominated populations systematically misrepresent elderly mobility behavior, particularly for spatial mobility metrics. The Markov model trained on the full population overestimates elderly step length by 4.5% and dwell time by 8.9%, whereas the elderly-specific model achieves substantially lower errors across most metrics. Comparisons between the Markov and LLM-based frameworks further show that higher-capability models do not necessarily improve subgroup-level fidelity under limited demographic data. These findings underscore the importance of demographic representation in mobility modeling and its downstream applications for underrepresented populations.

A Systematic Approach for Selecting Trajectories for Data Augmentation

Trajectory data augmentation is a promising approach to mitigate data scarcity in machine learning applications, but its utility has been limited by the complexity of preserving spatio-temporal coherence. Although prior work demonstrated the viability of geometric perturbation, it relied on naive random selection, leaving a critical gap in understanding which trajectories should be augmented for maximal benefit. This thesis addresses this gap by developing a systematic and scalable framework to evaluate five systematic selection strategies: Outlierness, Diversity, Representativeness, Uncertainty, and Random selection. These strategies were rigorously tested across four datasets covering animal behavior (Foxes and Starkey), maritime traffic (AIS), and urban traffic (Car) using a suite of linear and non-linear machine learning models. As part of this evaluation, an Optuna-based hyperparameter optimization loop was integrated to empirically identify the best-performing augmentation parameters for each dataset within the explored search space. The results indicate that, while systematic selection is not a universal solution, it offers distinct advantages over the random baseline. Systematic strategies, particularly Outlierness and Uncertainty, demonstrated higher stability and were less prone to performance degradation observed with random sampling in dense datasets. However, the findings also reveal that the value of augmentation is strictly conditional. Visual analysis via UMAP demonstrates that while systematic augmentation successfully repairs topological fragmentation in sparse datasets, it can act as a corrupting noise signal in high-quality, dense datasets. Furthermore, the study identified physical limitations in high-velocity domains, where standard perturbation techniques lead to divergence in feature space...