Aardvark Weather: end-to-end data-driven weather forecasting

Machine learning is revolutionising medium-range weather prediction. However it has only been applied to specific and individual components of the weather prediction pipeline. Consequently these data-driven approaches are unable to be deployed without input from conventional operational numerical weather prediction (NWP) systems, which is computationally costly and does not support end-to-end optimisation. In this work, we take a radically different approach and replace the entire NWP pipeline with a machine learning model. We present Aardvark Weather, the first end-to-end data-driven forecasting system which takes raw observations as input and provides both global and local forecasts. These global forecasts are produced for 24 variables at multiple pressure levels at one-degree spatial resolution and 24 hour temporal resolution, and are skillful with respect to hourly climatology at five to seven day lead times. Local forecasts are produced for temperature, mean sea level pressure, and wind speed at a geographically diverse set of weather stations, and are skillful with respect to an IFS-HRES interpolation baseline at multiple lead-times. Aardvark, by virtue of its simplicity and scalability, opens the door to a new paradigm for performing accurate and efficient data-driven medium-range weather forecasting.

Diffusion-Augmented Neural Processes

Over the last few years, Neural Processes have become a useful modelling tool in many application areas, such as healthcare and climate sciences, in which data are scarce and prediction uncertainty estimates are indispensable. However, the current state of the art in the field (AR CNPs; Bruinsma et al., 2023) presents a few issues that prevent its widespread deployment. This work proposes an alternative, diffusion-based approach to NPs which, through conditioning on noised datasets, addresses many of these limitations, whilst also exceeding SOTA performance.

Sim2Real for Environmental Neural Processes

Machine learning (ML)-based weather models have recently undergone rapid improvements. These models are typically trained on gridded reanalysis data from numerical data assimilation systems. However, reanalysis data comes with limitations, such as assumptions about physical laws and low spatiotemporal resolution. The gap between reanalysis and reality has sparked growing interest in training ML models directly on observations such as weather stations. Modelling scattered and sparse environmental observations requires scalable and flexible ML architectures, one of which is the convolutional conditional neural process (ConvCNP). ConvCNPs can learn to condition on both gridded and off-the-grid context data to make uncertainty-aware predictions at target locations. However, the sparsity of real observations presents a challenge for data-hungry deep learning models like the ConvCNP. One potential solution is 'Sim2Real': pre-training on reanalysis and fine-tuning on observational data. We analyse Sim2Real with a ConvCNP trained to interpolate surface air temperature over Germany, using varying numbers of weather stations for fine-tuning. On held-out weather stations, Sim2Real training substantially outperforms the same model architecture trained only with reanalysis data or only with station data, showing that reanalysis data can serve as a stepping stone for learning from real observations. Sim2Real could thus enable more accurate models for weather prediction and climate monitoring.

Active Learning with Convolutional Gaussian Neural Processes for Environmental Sensor Placement

Deploying environmental measurement stations can be a costly and time-consuming procedure, especially in remote regions that are difficult to access, such as Antarctica. Therefore, it is crucial that sensors are placed as efficiently as possible, maximising the informativeness of their measurements. This can be tackled by fitting a probabilistic model to existing data and identifying placements that would maximally reduce the model's uncertainty. The models most widely used for this purpose are Gaussian processes (GPs). However, designing a GP covariance which captures the complex behaviour of non-stationary spatiotemporal data is a difficult task. Further, the computational cost of GPs makes them challenging to scale to large environmental datasets. In this work, we explore using a convolutional Gaussian neural process (ConvGNP) to address these issues. A ConvGNP is a meta-learning model that uses neural networks to parameterise a GP predictive. Our model is data-driven, flexible, efficient, and permits multiple input predictors of gridded or scattered modalities. Using simulated surface air temperature fields over Antarctica as ground truth, we show that a ConvGNP significantly outperforms a non-stationary GP baseline in terms of predictive performance. We then use the ConvGNP in an Antarctic sensor placement toy experiment, yielding promising results.

Challenges and Pitfalls of Bayesian Unlearning

Machine unlearning refers to the task of removing a subset of training data, thereby removing its contributions to a trained model. Approximate unlearning are one class of methods for this task which avoid the need to retrain the model from scratch on the retained data. Bayes' rule can be used to cast approximate unlearning as an inference problem where the objective is to obtain the updated posterior by dividing out the likelihood of deleted data. However this has its own set of challenges as one often doesn't have access to the exact posterior of the model parameters. In this work we examine the use of the Laplace approximation and Variational Inference to obtain the updated posterior. With a neural network trained for a regression task as the guiding example, we draw insights on the applicability of Bayesian unlearning in practical scenarios.

Practical Conditional Neural Processes Via Tractable Dependent Predictions

Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learning models which leverage the flexibility of deep learning to produce well-calibrated predictions and naturally handle off-the-grid and missing data. CNPs scale to large datasets and train with ease. Due to these features, CNPs appear well-suited to tasks from environmental sciences or healthcare. Unfortunately, CNPs do not produce correlated predictions, making them fundamentally inappropriate for many estimation and decision making tasks. Predicting heat waves or floods, for example, requires modelling dependencies in temperature or precipitation over time and space. Existing approaches which model output dependencies, such as Neural Processes (NPs; Garnelo et al., 2018b) or the FullConvGNP (Bruinsma et al., 2021), are either complicated to train or prohibitively expensive. What is needed is an approach which provides dependent predictions, but is simple to train and computationally tractable. In this work, we present a new class of Neural Process models that make correlated predictions and support exact maximum likelihood training that is simple and scalable. We extend the proposed models by using invertible output transformations, to capture non-Gaussian output distributions. Our models can be used in downstream estimation tasks which require dependent function samples. By accounting for output dependencies, our models show improved predictive performance on a range of experiments with synthetic and real data.

Efficient Gaussian Neural Processes for Regression

Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood procedure. A limitation of CNPs is their inability to model dependencies in the outputs. This significantly hurts predictive performance and renders it impossible to draw coherent function samples, which limits the applicability of CNPs in down-stream applications and decision making. Neural Processes (NPs; Garnelo et al., 2018) attempt to alleviate this issue by using latent variables, relying on these to model output dependencies, but introduces difficulties stemming from approximate inference. One recent alternative (Bruinsma et al.,2021), which we refer to as the FullConvGNP, models dependencies in the predictions while still being trainable via exact maximum-likelihood. Unfortunately, the FullConvGNP relies on expensive 2D-dimensional convolutions, which limit its applicability to only one-dimensional data. In this work, we present an alternative way to model output dependencies which also lends itself maximum likelihood training but, unlike the FullConvGNP, can be scaled to two- and three-dimensional data. The proposed models exhibit good performance in synthetic experiments.

The Gaussian Neural Process

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to train conditional NPs. Moreover, we propose a new member to the Neural Process family called the Gaussian Neural Process (GNP), which models predictive correlations, incorporates translation equivariance, provides universal approximation guarantees, and demonstrates encouraging performance.

Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes

Stationary stochastic processes (SPs) are a key component of many probabilistic models, such as those for off-the-grid spatio-temporal data. They enable the statistical symmetry of underlying physical phenomena to be leveraged, thereby aiding generalization. Prediction in such models can be viewed as a translation equivariant map from observed data sets to predictive SPs, emphasizing the intimate relationship between stationarity and equivariance. Building on this, we propose the Convolutional Neural Process (ConvNP), which endows Neural Processes (NPs) with translation equivariance and extends convolutional conditional NPs to allow for dependencies in the predictive distribution. The latter enables ConvNPs to be deployed in settings which require coherent samples, such as Thompson sampling or conditional image completion. Moreover, we propose a new maximum-likelihood objective to replace the standard ELBO objective in NPs, which conceptually simplifies the framework and empirically improves performance. We demonstrate the strong performance and generalization capabilities of ConvNPs on 1D regression, image completion, and various tasks with real-world spatio-temporal data.