Two years ago, as part of the Department of Mathematical Sciences at NTNU, I was awarded postdoctoral fellowship funding under an MSCA from the European Commission. Since then, I’ve been happy to see an increasing number of successful applications in the department and thoroughly recommend the program to interested early-career researchers.
Together with my supervisor, Elena Celledoni, and collaborators from both academia and industry, we aim to improve weather forecasting using neural networks. Great strides have been made recently in weather forecastings with Google’s GraphCast, which has proven a powerful (and useful) tool. Our thesis differs in one key aspect: We aim to use neural networks to enhance existing technologies (as opposed to replacing them).
Weather forecasting has long involved many difficult-to-simulate phenomena (such as cloud coverage) and requires continuous integration with data (through data assimilation). At its core, a forecasting model is driven by simulating fluid dynamics. It is within these fluid dynamic simulations which we find ourselves. To obtain a locally accurate forecast, our simulation must be highly resolved. Unfortunately, running the model at a high resolution leads to the model runtime becoming slower than real-time, rendering the forecast obsolete. This leads us to consider a limited area model (LAM), which simulates at a higher resolution over a smaller region of interest, for example, Northern Europe[1]. This allows us to run at a higher resolution than possible with a global model faster than real time.
There is one fundamental problem with LAMs: the boundary conditions. When restricting to a limited area, one must allow weather patterns to flow into the domain. Due to the atmosphere’s multiscale nature, phenomena that occur at a fine resolution (such as vortices and eddies) will not appear on the poorly resolved global model. Indeed, if our boundary data lacks these fine-grain phenomena, this will typically lead to unrealistic behaviour near the boundaries of the LAM, polluting the simulation. We aim to bridge this gap with convolutional neural networks in a simplified setup, which can be read about in a proceedings article to appear at the end of this month[2]. While still under development, we are now delving into the world of graph neural networks to move our approach to a more general setting.
LAMs are not the only methodology for improving the time to solution for a well-resolved forecast. By developing advanced solvers that exploit highly parallelisable algorithms, we may improve the runtime of atmospheric simulations[3]. Conversely, we may also utilise neural networks to assist with learning aspects of solution dynamics at a significantly lower cost[4]. These are two minor avenues this project has allowed me to explore to improve our forecasting capabilities, and I am very grateful to the European Commission for this opportunity.
[1] Bush et al., “The First Met Office Unified Model–JULES Regional Atmosphere and Land Configuration, RAL1”, Geosc. Model Dev., 2020.
[2] Jackaman and Sutton, “Improving Regional Weather Forecasts with Neural Interpolation”, International conference on Scientific Computing and Machine Learning (to appear), 2025.
[3] Jackaman and MacLachlan, “Space-Time Waveform Relaxation Multigrid for Navier-Stokes”, (in review), 2024.
[4] Celledoni et al., “Predictions Based on Pixel Data”, (in review), 2024.