AeroMELD: A Linear Embedding of Aerosol Populations for Diagnostics and Latent Dynamics

Accurately representing atmospheric aerosol populations is essential for simulating aerosol-cloud interactions, radiative forcing, and ice nucleation, yet existing reduced schemes impose structural assumptions that limit their ability to capture composition diversity and mixing state. Machine-learning approaches offer more flexible representations, but standard autoencoders do not preserve the mathematical structure of aerosol populations and therefore cannot support physically meaningful process operators. We introduce AeroMELD (Aerosol Measure Embedding for Latent Dynamics), a mathematically grounded framework for constructing low-dimensional latent variables that retain this structure. We show that any permutation-invariant linear encoder must take a scale-shape decomposition, with total number concentration represented explicitly and latent shape given by a barycentric combination of per-particle embeddings. This aggregated latent state retains the diagnostic expressiveness of a Deep Sets model by moving the nonlinear post-aggregation stage into the learned diagnostic map while preserving latent linearity. Using particle-resolved data as ground truth, we encode weighted particle populations directly rather than binned aerosol states; size-resolved mass and number distributions serve only as diagnostic targets and visual summaries. The latent space accurately reconstructs these distributions, CCN spectra, optical coefficients, and immersion-freezing behavior while preserving the linear population structure needed for hybrid ML-physics models. Although the experiments focus on diagnostic reconstruction, the embedding is designed so that emissions and mixing can be represented exactly and nonlinear microphysical processes learned in a controlled latent space. This work establishes a foundation for learning aerosol-process evolution directly in latent space.

Unsupervised Regionalization of Particle-resolved Aerosol Mixing State Indices on the Global Scale

The aerosol mixing state significantly affects the climate and health impacts of atmospheric aerosol particles. Simplified aerosol mixing state assumptions, common in Earth System models, can introduce errors in the prediction of these aerosol impacts. The aerosol mixing state index, a metric to quantify aerosol mixing state, is a convenient measure for quantifying these errors. Global estimates of aerosol mixing state indices have recently become available via supervised learning models, but require regionalization to ease spatiotemporal analysis. Here we developed a simple but effective unsupervised learning approach to regionalize predictions of global aerosol mixing state indices. We used the monthly average of aerosol mixing state indices global distribution as the input data. Grid cells were then clustered into regions by the k-means algorithm without explicit spatial information as input. This approach resulted in eleven regions over the globe with specific spatial aggregation patterns. Each region exhibited a unique distribution of mixing state indices and aerosol compositions, showing the effectiveness of the unsupervised regionalization approach. This study defines "aerosol mixing state zones" that could be useful for atmospheric science research.