RAIN: Reinforcement Algorithms for Improving Numerical Weather and Climate Models

This study explores integrating reinforcement learning (RL) with idealised climate models to address key parameterisation challenges in climate science. Current climate models rely on complex mathematical parameterisations to represent sub-grid scale processes, which can introduce substantial uncertainties. RL offers capabilities to enhance these parameterisation schemes, including direct interaction, handling sparse or delayed feedback, continuous online learning, and long-term optimisation. We evaluate the performance of eight RL algorithms on two idealised environments: one for temperature bias correction, another for radiative-convective equilibrium (RCE) imitating real-world computational constraints. Results show different RL approaches excel in different climate scenarios with exploration algorithms performing better in bias correction, while exploitation algorithms proving more effective for RCE. These findings support the potential of RL-based parameterisation schemes to be integrated into global climate models, improving accuracy and efficiency in capturing complex climate dynamics. Overall, this work represents an important first step towards leveraging RL to enhance climate model accuracy, critical for improving climate understanding and predictions. Code accessible at https://github.com/p3jitnath/climate-rl.

Linear combinations of latents in diffusion models: interpolation and beyond

Generative models are crucial for applications like data synthesis and augmentation. Diffusion, Flow Matching and Continuous Normalizing Flows have shown effectiveness across various modalities, and rely on Gaussian latent variables for generation. As any generated object is directly associated with a particular latent variable, we can manipulate the variables to exert control over the generation process. However, standard approaches for combining latent variables, such as spherical interpolation, only apply or work well in special cases. Moreover, current methods for obtaining low-dimensional representations of the data, important for e.g. surrogate models for search and creative applications, are network and data modality specific. In this work we show that the standard methods to combine variables do not yield intermediates following the distribution the models are trained to expect. We propose Combination of Gaussian variables (COG), a novel interpolation method that addresses this, is easy to implement yet matches or improves upon current methods. COG addresses linear combinations in general and, as we demonstrate, also supports other operations including e.g. defining subspaces of the latent space, simplifying the creation of expressive low-dimensional spaces of high-dimensional objects using generative models based on Gaussian latents.

Efficient modeling of sub-kilometer surface wind with Gaussian processes and neural networks

Accurately representing surface weather at the sub-kilometer scale is crucial for optimal decision-making in a wide range of applications. This motivates the use of statistical techniques to provide accurate and calibrated probabilistic predictions at a lower cost compared to numerical simulations. Wind represents a particularly challenging variable to model due to its high spatial and temporal variability. This paper presents a novel approach that integrates Gaussian processes (GPs) and neural networks to model surface wind gusts, leveraging multiple data sources, including numerical weather prediction (NWP) models, digital elevation models (DEM), and in-situ measurements. Results demonstrate the added value of modeling the multivariate covariance structure of the variable of interest, as opposed to only applying a univariate probabilistic regression approach. Modeling the covariance enables the optimal integration of observed measurements from ground stations, which is shown to reduce the continuous ranked probability score compared to the baseline. Moreover, it allows the direct generation of realistic fields that are also marginally calibrated, aided by scalable techniques such as Random Fourier Features (RFF) and pathwise conditioning. We discuss the effect of different modeling choices, as well as different degrees of approximation, and present our results for a case study.

Fantasizing with Dual GPs in Bayesian Optimization and Active Learning

Gaussian processes (GPs) are the main surrogate functions used for sequential modelling such as Bayesian Optimization and Active Learning. Their drawbacks are poor scaling with data and the need to run an optimization loop when using a non-Gaussian likelihood. In this paper, we focus on `fantasizing' batch acquisition functions that need the ability to condition on new fantasized data computationally efficiently. By using a sparse Dual GP parameterization, we gain linear scaling with batch size as well as one-step updates for non-Gaussian likelihoods, thus extending sparse models to greedy batch fantasizing acquisition functions.