  Accurately forecasting urban development and its environmental and climate
impacts critically depends on realistic models of the spatial structure of the
built environment, and of its dependence on key factors such as population and
economic development. Scenario simulation and sensitivity analysis, i.e.,
predicting how changes in underlying factors at a given location affect
urbanization outcomes at other locations, is currently not achievable at a
large scale with traditional urban growth models, which are either too
simplistic, or depend on detailed locally-collected socioeconomic data that is
not available in most places. Here we develop a framework to estimate, purely
from globally-available remote-sensing data and without parametric assumptions,
the spatial sensitivity of the (\textit{static}) rate of change of urban sprawl
to key macroeconomic development indicators. We formulate this spatial
regression problem as an image-to-image translation task using conditional
generative adversarial networks (GANs), where the gradients necessary for
comparative static analysis are provided by the backpropagation algorithm used
to train the model. This framework allows to naturally incorporate physical
constraints, e.g., the inability to build over water bodies. To validate the
spatial structure of model-generated built environment distributions, we use
spatial statistics commonly used in urban form analysis. We apply our method to
a novel dataset comprising of layers on the built environment, nightlighs
measurements (a proxy for economic development and energy use), and population
density for the world's most populous 15,000 cities.
