  Urban areas are a high-stake target of climate change mitigation and
adaptation measures. To understand, predict and improve the energy performance
of cities, the scientific community develops numerical models that describe how
they interact with the atmosphere through heat and moisture exchanges at all
scales. In this review, we present recent advances that are at the origin of
last decade's revolution in computer graphics, and recent breakthroughs in
statistical physics that extend well established path-integral formulations to
non-linear coupled models. We argue that this rare conjunction of scientific
advances in mathematics, physics, computer and engineering sciences opens
promising avenues for urban climate modeling and illustrate this with coupled
heat transfer simulations in complex urban geometries under complex atmospheric
conditions. We highlight the potential of these approaches beyond urban climate
modeling, for the necessary appropriation of the issues at the heart of the
energy transition by societies.
