Speaker
Description
Classical dimensionality reduction has served physics well. PCA is fast, transparent, and cleanly ranks structures by explained variance, which is why it remains the default first look for almost any high-dimensional dataset. But its strengths come from assumptions the underlying physics rarely respects, the modes must be linear and mutually orthogonal, forcing genuinely distinct physical states to be smeared across several components or merged into one. Unsupervised methods such as clustering or vanilla autoencoders relax these constraints, yet they introduce a different problem: they find whatever structure dominates the input, with no guarantee that it bears any relation to the quantity we actually care about. How do we then tease out non-linear, non-orthogonal, and non-dominant, but still relevant, structures in our data?
As a possible answer to this question, we present a Regression Mixture Model Convolutional Variational Autoencoder (RMM-CVAE). A CNN encoder compresses input fields into a low-dimensional latent space with a mixture-of-Gaussians prior, so that each mixture component corresponds to an interpretable regime. A regression head trained jointly with the autoencoder ties the latent space to a target variable, making the discovered regimes informative about impacts rather than merely about input similarity. Because the model is generative, each regime can be decoded back into physical space and inspected directly. Along the way, we discuss the practical lessons that transfer beyond our application: keeping mixture-prior VAEs stable during training and choosing the right output distribution for skewed, zero-heavy data.
As a demonstration, we apply the framework to a problem from climate physics: discovering large-scale atmospheric patterns from daily sea-level pressure fields that drive precipitation in Europe. The model recovers well-known circulation patterns, alongside regimes that linear methods cannot separate, and links each of them to its regional rainfall fingerprint. The same recipe should be applicable wherever interpretable latent states must be connected to physical outcomes.