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.

Data-informed lifting line theory

We present a data-driven framework that extends the predictive capability of classical lifting-line theory (LLT) to a wider aerodynamic regime by incorporating higher-fidelity aerodynamic data from panel method simulations. A neural network architecture with a convolutional layer followed by fully connected layers is developed, comprising two parallel subnetworks to separately process spanwise collocation points and global geometric/aerodynamic inputs such as angle of attack, chord, twist, airfoil distribution, and sweep. Among several configurations tested, this architecture is most effective in learning corrections to LLT outputs. The trained model captures higher-order three-dimensional effects in spanwise lift and drag distributions in regimes where LLT is inaccurate, such as low aspect ratios and high sweep, and generalizes well to wing configurations outside both the LLT regime and the training data range. The method retains LLT's computational efficiency, enabling integration into aerodynamic optimization loops and early-stage aircraft design studies. This approach offers a practical path for embedding high-fidelity corrections into low-order methods and may be extended to other aerodynamic prediction tasks, such as propeller performance.