Uncertainty Quantification for Reduced-Order Surrogate Models Applied to Cloud Microphysics

TL;DR

Uncertainty quantification for latent-space reduced-order models of cloud microphysics is challenging and often tied to specific architectures. The authors propose a post hoc, model-agnostic UQ pipeline based on conformal prediction to produce distribution-free predictive intervals for reconstruction, latent dynamics, and end-to-end predictions in latent-space ROMs, demonstrated on an AE–SINDy surrogate trained on PSDs from LES with the superdroplet method. The framework uses tailwise conformal intervals for DSD outputs and Mahalanobis-distance-based latent-space intervals, comparing Vanilla, Split, and CV+ CP schemes, and analyzes how uncertainty propagates through reconstruction, latent dynamics, and end-to-end forecasts. This work enables principled, scalable uncertainty assessment for fast surrogate models in cloud microphysics, with potential broad applicability to other physics ROMs and climate-scale modeling.

Abstract

Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and generalization. We introduce a post hoc, model-agnostic framework for predictive uncertainty quantification in latent space ROMs that requires no modification to the underlying architecture or training procedure. Using conformal prediction, our approach estimates statistical prediction intervals for multiple components of the ROM pipeline: latent dynamics, reconstruction, and end-to-end predictions. We demonstrate the method on a latent space dynamical model for cloud microphysics, where it accurately predicts the evolution of droplet-size distributions and quantifies uncertainty across the ROM pipeline.

Figures (3)

• Figure 1: A generic latent-space dynamical model with fixed dynamical time-step $\Delta t$. Figures 1a and 1b show the reconstruction and dynamics sub-models, respectively, that comprise the end-to-end model architecture shown in Figure 1c.
• Figure 2: Initial and final states for three sample DSD trajectories from the dataset, predicted using the trained AE-SINDy architecture ("Model") with empirical prediction intervals provided via CV+ conformal predictions (using $k=20$ folds) at varying nominal coverage levels. These predictions are also compared with the actual DSD final states from the dataset ("Data").
• Figure 3: Average prediction interval width vs. time, computed by applying vanilla CP, split CP (using a $60$-$20$-$20$ train-validation-test split), and CV+ conformal predictions (using $k=20$ folds), respectively, to the indicated components of the AE-SINDy pipeline at varying nominal coverage levels $1-\alpha$. Interval widths are computed using the mass-normalized integral of the area between prediction bands across bins for DSD-valued predictions and the volume of the Mahalanobis distance-derived prediction ellipsoids for latent-space predictions.