Downscaling using Physics Informed Neural Networks for model evaluation at urban scale

Cities contain a significant proportion of the global population. Because of their unique vulnerabilities to climate-related phenomena, such as the Urban Heat Island effect, understanding urban microclimates is essential to the durable safety and well-being of residents. However, global and regional climate models operate at scales too coarse to capture urban-scale processes. Accurately modeling urban microclimates requires resolving fine-scale details, such as the geometry and arrangement of buildings. Such high-resolution simulations entail substantial computational costs, which severely limit their applicability. Because of this, at this time, real-time prediction and design optimization problems remain mostly inaccessible. Therefore, there is a need for computationally efficient urban microclimate models.

The DANTE project aims to address this need by applying model order reduction techniques to high-resolution urban-scale simulations. Resulting models must undergo a rigorous validation process before any application is possible, to ensure accuracy and reliability 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.

The goal of our work is to construct a downscaling framework adapted to the context of weather data, leveraging regional model data, weather station measurements, as well as physical knowledge. In this context, pre-existing high-resolution data is very limited, rendering purely statistical downscaling approaches unsuitable. Since no models - other than those intended for evaluation - are available at the target scale, dynamical downscaling methods are also inadapted. Finally, the inhomogeneity of relevant scales, and the need to integrate data at arbitrary locations requires the use of irregular, variable grids.

A promising approach is to use Physics-Informed Neural Networks (PINNs). PINNs incorporate physical constraints into the learning process by including partial differential equation residuals into the loss function. By using networks that take coordinates as input and output the local system state, a fitted model can be evaluated at arbitrary locations, providing a way to downscale without need for a structured grid.

A major limitation of PINNs is their lack of robustness during training, as convergence can be difficult to achieve reliably. A contributing factor is that different loss terms can have wildly different scales and convergence rates, which can hinder optimization. Previous studies have explored strategies to make convergence more likely, but such results do not always generalize are are typically task and problem-specific.

In this work, we investigate the applicability of PINNs to the downscaling of weather data, formulated as a fluid dynamics problem on unstructured meshes. We assess the performance levels that can be achieved and examine the methodological choices that influence them, including network architecture, collocation point density, loss-term weighting strategies, data preprocessing, and training protocols. We also analyse the associated difficulties, computational costs, and practical requirements, and quantify the added value of the inclusion of physical knowledge.