Jürgen Hackl

Timothy LaRock, Chen Zhang, Jürgen Hackl

The detailed study of individual human mobility requires large-scale high-resolution datasets, but collecting such datasets in a way that is both statistically powerful and privacy preserving is a challenging and expensive task. In response, researchers have built tools to generate complex synthetic populations of agents that can be used to simulate synthetic individual mobility data, potentially obviating the difficulties of data collection. While these simulation-based approaches offer a promising avenue for expanding individual mobility research, it is difficult to asses whether such tools are effective at generating realistic mobility traces. In this work, we develop a framework for comparing observed and simulated mobility data using a higher-order network framework that focuses on analyzing patterns of movement in the paths individuals take through the underlying infrastructure network. We apply our framework to a case study comparing the NetMob 2025 Data Challenge Dataset, which includes individual mobility data for thousands of residents of the Île-de-France region, with a sophisticated open-source synthetic population and mobility simulation model of the same region. We show that while simulated mobility data is indeed promising as a surrogate for observed mobility, there are some key limitations to the simulation paradigm from a path-based perspective, which we discuss along with potential future remediations and open challenges for higher-order mobility network analysis.

Esmaeil Ghorbani, Jürgen Hackl

Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are heterogeneous, sensing is partial, uncertainty is distributed across subsystem interfaces, and computational cost grows rapidly with system size. We address this challenge with probabilistic compositional inference, a graph-based architecture that represents a coupled system as interacting subsystems, each retaining its own local model, estimator, and uncertainty representation, while coupling is handled through physically meaningful stochastic messages exchanged across subsystem interfaces. This formulation allows mechanistic, learned, and deterministic components to coexist within a single inference framework and propagates calibrated uncertainty without assembling a global augmented state or covariance. We validate the framework in three increasingly demanding settings: a sparse-sensing canonical inverse problem, where interface couplings can also be learned from data; infrastructure-scale power networks, where the method matches centralized joint state-and-parameter inference while reducing computational scaling from approximately cubic to approximately linear; and a multi-physics turbine embedded in a power-grid network, where heterogeneous subsystems compose hierarchically without degrading local inference or collapsing local posteriors into a global estimate. Together, these results show that subsystem structure can be exploited as the organizing principle for uncertainty-aware inverse inference in coupled engineered systems.

Xudong Fan, Jürgen Hackl

Spatially embedded networks (SENs) represent a special type of complex graph, whose topologies are constrained by the networks' embedded spatial environments. The graph representation of such networks is thereby influenced by the embedded spatial features of both nodes and edges. Accurate network representation of the graph structure and graph features is a fundamental task for various graph-related tasks. In this study, a Generic Multimodal Spatially Graph Convolutional Network (GMu-SGCN) is developed for efficient representation of spatially embedded networks. The developed GMu-SGCN model has the ability to learn the node connection pattern via multimodal node and edge features. In order to evaluate the developed model, a river network dataset and a power network dataset have been used as test beds. The river network represents the naturally developed SENs, whereas the power network represents a man-made network. Both types of networks are heavily constrained by the spatial environments and uncertainties from nature. Comprehensive evaluation analysis shows the developed GMu-SGCN can improve accuracy of the edge existence prediction task by 37.1\% compared to a GraphSAGE model which only considers the node's position feature in a power network test bed. Our model demonstrates the importance of considering the multidimensional spatial feature for spatially embedded network representation.