Artificial intelligence (AI) is transforming weather and climate modeling. For example, neural network-based weather models can now outperform physics-based models for up to 15-day forecasts at a fraction of the computing time. However, these AI models have challenges with learning the rarest yet most impactful weather extremes, particularly the gray swans (i.e., physically possible events so rare they have never been seen in the training set). They also poorly learn multi-scale chaotic dynamics. I will discuss some of these challenges, as well as some of the surprising capabilities of these models, e.g., transferring what they learn from one region to another for dynamically similar event. I will present ideas around integrating tools from applied math, climate physics, and AI to address some of these challenges and make progress. In particular, I will discuss the use if rare event sampling algorithms and the Fourier transform and adjoint of the deep neural networks.
