This was part of Machine Learning for Climate and Weather Applications

Integrating the spectral analysis of neural networks and nonlinear physics for explainability, generalizability, and stability

Pedram Hassanzadeh, Rice University

Friday, November 4, 2022

Abstract: The atmospheric and oceanic turbulent circulations involve a variety of nonlinearly interacting physical processes spanning a broad range of spatial and temporal scales. To make simulations of these turbulent flows computationally tractable, processes with scales smaller than the typical grid size of weather/climate models have to be parameterized. Recently, there has been substantial interest (and progress) in using deep learning techniques to develop data-driven subgrid-scale (SGS) parameterizations for the climate system. Another approach that is rapidly gaining popularity is to learn the entire spatio-temporal variability of the climate system from data, i.e., developing fully data-driven forecast models or emulators. For either of these approaches to be useful and reliable in practice, a number of major challenges have to be addressed. These include: 1) instabilities or unphysical drifts, 2) learning in the small-data regime, 3) interpretability, and 4) extrapolation to different parameters. Using several setups of 2D turbulence, two-layer quasi-geostrophic turbulence, Rayleigh-Benard convection, and ERA5 reanalysis, we introduce methods to address (1)-(4). The key aspect of some of these methods is combining the spectral analyses of deep neural networks and turbulence/nonlinear physics, as well as leveraging recent advances in theory and applications of deep learning. . In the end, we will discuss scaling up these methods to more complex systems and real-world applications, e.g., for SGS modeling of atmospheric gravity waves and conducting short- and long-term weather forecasting.