Downscaling using physics informed neural networks for model evaluation at urban scale

Cities contain a significant proportion of the global population. As they are subjected to unique vulnerabilities to climate-related phenomena, such as the Urban heat Island effect, it is crucial for ensuring the durable safety of city residents to understand urban microclimate. However, global and regional climate models operate at scales too coarse to capture the intricacies of these microclimates. Accurately modeling them requires resolving fine-scale details, including the shape and arrangement of buildings. Unfortunately, such high-resolution simulations come with a substantial computational cost, which limits their applicability, making real-time prediction and design optimization problems mainly inaccessible. Therefore, there is a need for computationally efficient models of urban microclimate.

The DANTE project aims to address this challenge by applying Model Order Reduction (MOR) techniques to lower the computational costs associated with high-resolution urban-scale simulations. MOR involves replacing full-order models - here, detailed Computational Fluid Dynamics (CFD) simulations - with reduced-order models of lower complexity. These models can be derived either by projection of the full-order model onto lower-dimensional manifolds, or through machine learning methodologies.

Regardless of the approach, these models must undergo a rigorous validation process before any application is possible to ensure that they accurately reproduce relevant physical properties. Furthermore, evaluating their performance and quantifying their uncertainties is essential to determine the reliability of their output for real world applications. This validation process requires urban-scale ground truth data, which is not directly available. Instead, lower-resolution data must be downscaled to urban scale. As a result, downscaling is a critical part of developing reliable urban microclimate models.

Traditional statistical downscaling methods rely on large datasets to establish mappings from low-resolution to high-resolution data, but in this context, data is scarce. One solution to this problem is Physics-Informed Neural Networks (PINN), which incorporate physical constraints into the learning process, thereby alleviating data requirements. By enforcing, through a choice of loss function, a set of physical partial differential equations, PINNs are able to more efficiently extract relevant information from the data. They can be used for prediction, but also as continuous function approximators for downscaling data. In this work, we propose a downscaling framework that leverages PINNs to assimilate both regional model data and weather station measurements, generating urban-scale data suitable for evaluating reduced-order models.