A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data

TL;DR

This work presents a general strategy for training variational (probabilistic) neural network models to non‐intrusively correct under‐resolved long‐time simulations of turbulent climate systems and demonstrates significant improvement over previously introduced deterministic architectures.

Abstract

Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a consequence, the spatiotemporal resolution required for accurate simulation of these systems is typically computationally infeasible, particularly for applications of long-term risk assessment, such as the quantification of extreme weather risk due to climate change. While data-driven modeling offers some promise of alleviating these obstacles, the scarcity of high-quality simulations results in limited available data to train such models, which is often compounded by the lack of stability for long-horizon simulations. As such, the computational, algorithmic, and data restrictions generally imply that the probability of rare extreme events is not accurately captured. In this work we present a general strategy for training neural network models to non-intrusively correct under-resolved long-time simulations of chaotic systems. The approach is based on training a post-processing correction operator on under-resolved simulations nudged towards a high-fidelity reference. This enables us to learn the dynamics of the underlying system directly, which allows us to use very little training data, even when the statistics thereof are far from converged. Additionally, through the use of probabilistic network architectures we are able to leverage the uncertainty due to the limited training data to further improve extrapolation capabilities. We apply our framework to severely under-resolved simulations of quasi-geostrophic flow and demonstrate its ability to accurately predict the anisotropic statistics over time horizons more than 30 times longer than the data seen in training.

Figures (18)

• Figure 1: Diagram of the nudging-based machine learning framework.
• Figure 2: Zonal average (a) and normalized covariance (b) of the lower layer stream function $\psi_2$ of the RD and CR data sets. Illustration of the bottom topography profile (c).
• Figure 3: Graphical model and recursive evaluation equations for the four network architectures considered in this work: basic RNN (a), VAE-RNN (b), STORN (c), VRNN (d). Latent space dependencies upstream and downstream of the recurrent layer are marked red and green respectively.
• Figure 4: Global pdf, log-pdf, and PSD of $\psi_1$ (upper panel) and $\psi_2$ (lower panel). RD (solid black), CR (dashed black), RNN (red), VAE-RNN (green), STORN (blue), VRNN (teal).
• Figure 5: Ground truth reference statistics of 34,000 time unit test data (black) and 1,000 time unit training data (magenta) of $\psi_1$ (a) and $\psi_2$ (b). Each subfigure shows the pdf on linear and logarithmic scale.