Graph Neural Ordinary Differential Equations for Coarse-Grained Socioeconomic Dynamics

TL;DR

This work tackles the challenge of modeling space-time socioeconomic dynamics by bridging high-fidelity ABMs with a tractable, coarse-grained equation-based model. It introduces a graph-based Neural ODE surrogate that learns a closure for population flux on a network, enabling differentiable, fast simulations of coarse-grained dynamics while preserving essential behaviors. The Baltimore CHANCE-C case study demonstrates good qualitative and quantitative agreement (approximately $10.5\%$ MAPE and $MAE \approx 25.1k$) and yields dramatic speedups (≈$5\times 10^{4}$) over the full ABM, with accurate capture of outmigration onset. The approach offers practical benefits for surrogate modeling, ABM calibration, hybrid ABM-EBM workflows, and digital twins, supporting rapid scenario analysis, policy design, and resilience planning in coastal urban systems.

Abstract

We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic relationships -- in the form of ordinary differential equations -- while preserving critical system behaviors. This approach allows for expedited 'what if' studies and sensitivity analyses, essential for informed policy-making. Our findings, from a case study of Baltimore, MD, indicate that this machine learning-augmented coarse-grained model serves as a powerful instrument for deciphering the complex interactions between social factors, geography, and exogenous stressors, offering a valuable asset for system forecasting and resilience planning.

Figures (8)

• Figure 1: In (a), Balitimore County, MD is displayed as the composition of individual census block groups that contain people and housing. These data can be spatially aggregated (e.g. based on distance to the city center, as is depicted in (b)) into zones and equivalently represented as nodes on a graph. In this example, the edges between the nodes represent migration pathways. The population contained in these nodes can be similarly aggregated into socioeconomic groups; e.g. low, middle, and high income sub-populations, as is shown in (c).
• Figure 2: After aggregation into nodes in a graph, one can associate states and features to each node. In (a), the definition for the nodes is depicted. Each has capacity for housing, denoted $C$. A mixture of the three sub-populations (low, middle, and high income groups) occupy a fraction of the available housing. The node's states are defined by the composition of the sub-populations. The nodal features are attributes that are specified or derived from model states. Here, they are mixture fraction, a notion of pressure, and a latent variable $q$ to act as a 'catch-all' feature. The EBM evolves the states with an ODE solver, as shown in (b). This evolution procedure is differentiable, meaning the parameters of the model can be automatically tuned to minimize an objective function with a gradient-based optimizer.
• Figure 3: Model training history. 'Best Model' is selected as the weights that minimize the loss for the validation set.
• Figure 4: A protoypical experiment output (taken from test set). Population dynamics on the nodes exhibit complex, nonlinear behaviors. The EBM is able to qualitatively reproduce these trends for each data trace. Over the duration of the experiment, the EBM has a 10.5% Mean Absolute Percentage Error.
• Figure 5: In addition to tracking flux between Urban/Sub-Urban/Rural nodes, the EBM can also track outmigration. Shown here is the onset of outmigration at approximately 10 years into the model simulation.