Towards diffusion models for large-scale sea-ice modelling

TL;DR

The paper addresses the challenge of generating Arctic-wide sea-ice states with physical bounds in a computationally efficient way. It develops latent diffusion models (LDMs) that map high-dimensional sea-ice fields to a latent space via a variational autoencoder and enforce bounds through a censored Gaussian reconstruction loss, comparing them to diffusion in data space. Key findings show that LDMs achieve competitive scores while producing smoother fields, with censoring improving the representation of the marginal ice zone and physical consistency, and that LDMs are about 25 times faster than data-space diffusion. The work demonstrates a viable pathway for large-scale Earth system surrogates and surrogate modelling, while noting smoothing remains a barrier and outlining potential improvements and extensions to other Earth system components.

Abstract

We make the first steps towards diffusion models for unconditional generation of multivariate and Arctic-wide sea-ice states. While targeting to reduce the computational costs by diffusion in latent space, latent diffusion models also offer the possibility to integrate physical knowledge into the generation process. We tailor latent diffusion models to sea-ice physics with a censored Gaussian distribution in data space to generate data that follows the physical bounds of the modelled variables. Our latent diffusion models reach similar scores as the diffusion model trained in data space, but they smooth the generated fields as caused by the latent mapping. While enforcing physical bounds cannot reduce the smoothing, it improves the representation of the marginal ice zone. Therefore, for large-scale Earth system modelling, latent diffusion models can have many advantages compared to diffusion in data space if the significant barrier of smoothing can be resolved.

Figures (5)

• Figure 1: Samples generated with a diffusion model in data space (a--d) and a latent diffusion model with censoring (e--h). The thickness (a, e) and concentration (b, f) are directly generated, while the speed (c, g) and deformation (d, h) are derived from the velocities. Note, for visualisation purpose, only the central Arctic is shown while the whole Arctic is modelled. The remaining noise might be caused by using only 20 integration steps with a Heun sampler.
• Figure 2: Estimated spectral density of the sea-ice thickness in the central Arctic for the testing dataset (black), an autoencoder ($\beta=10^{-3}$, no censoring, light blue), the LDM learned in the latent space of the autoencoder (dark blue), and the diffusion model directly learned in data space (red).
• Figure 3: Estimated spectral density of the sea-ice thickness in the central Arctic for the testing dataset (black), and three different hyperparameter configurations for the autoencoder.
• Figure 4: Comparison of the probabilities that a grid point is covered by sea-ice as seen in the testing dataset or as predicted by the validation dataset (gray), the diffusion model in data space (red, Diff), the latent diffusion model (blue, LDM), and the latent diffusion model with censoring (yellow). The shown probabilities represent the averaged predicted probabilities, grouped into $5\,\%$ intervals based on the test probabilities.
• Figure 5: Uncurated samples from the diffusion model in data space (a--d), the latent diffusion model without censoring (e--h), and the latent diffusion model with censoring (i--l), and the neXtSIM simulations. As in Fig. \ref{['fig:samples']}, the thickness and concentration are directly generated, while the speed and deformation are derived from the generated velocities. Best to view in digital and colour.