J. Scott Hosking

Wessel P. Bruinsma, Stratis Markou, James Requiema et al.

Conditional neural processes (CNPs; Garnelo et al., 2018a) are attractive meta-learning models which produce well-calibrated predictions and are trainable via a simple maximum likelihood procedure. Although CNPs have many advantages, they are unable to model dependencies in their predictions. Various works propose solutions to this, but these come at the cost of either requiring approximate inference or being limited to Gaussian predictions. In this work, we instead propose to change how CNPs are deployed at test time, without any modifications to the model or training procedure. Instead of making predictions independently for every target point, we autoregressively define a joint predictive distribution using the chain rule of probability, taking inspiration from the neural autoregressive density estimator (NADE) literature. We show that this simple procedure allows factorised Gaussian CNPs to model highly dependent, non-Gaussian predictive distributions. Perhaps surprisingly, in an extensive range of tasks with synthetic and real data, we show that CNPs in autoregressive (AR) mode not only significantly outperform non-AR CNPs, but are also competitive with more sophisticated models that are significantly more computationally expensive and challenging to train. This performance is remarkable given that AR CNPs are not trained to model joint dependencies. Our work provides an example of how ideas from neural distribution estimation can benefit neural processes, and motivates research into the AR deployment of other neural process models.

Aditya Ravuri, Tom R. Andersson, Ieva Kazlauskaite et al. · cambridge

Ice cores record crucial information about past climate. However, before ice core data can have scientific value, the chronology must be inferred by estimating the age as a function of depth. Under certain conditions, chemicals locked in the ice display quasi-periodic cycles that delineate annual layers. Manually counting these noisy seasonal patterns to infer the chronology can be an imperfect and time-consuming process, and does not capture uncertainty in a principled fashion. In addition, several ice cores may be collected from a region, introducing an aspect of spatial correlation between them. We present an exploration of the use of probabilistic models for automatic dating of ice cores, using probabilistic programming to showcase its use for prototyping, automatic inference and maintainability, and demonstrate common failure modes of these tools.

Tom R. Andersson, Wessel P. Bruinsma, Stratis Markou et al.

Environmental sensors are crucial for monitoring weather conditions and the impacts of climate change. However, it is challenging to place sensors in a way that maximises the informativeness of their measurements, particularly in remote regions like Antarctica. Probabilistic machine learning models can suggest informative sensor placements by finding sites that maximally reduce prediction uncertainty. Gaussian process (GP) models are widely used for this purpose, but they struggle with capturing complex non-stationary behaviour and scaling to large datasets. This paper proposes using a convolutional Gaussian neural process (ConvGNP) to address these issues. A ConvGNP uses neural networks to parameterise a joint Gaussian distribution at arbitrary target locations, enabling flexibility and scalability. Using simulated surface air temperature anomaly over Antarctica as training data, the ConvGNP learns spatial and seasonal non-stationarities, outperforming a non-stationary GP baseline. In a simulated sensor placement experiment, the ConvGNP better predicts the performance boost obtained from new observations than GP baselines, leading to more informative sensor placements. We contrast our approach with physics-based sensor placement methods and propose future steps towards an operational sensor placement recommendation system. Our work could help to realise environmental digital twins that actively direct measurement sampling to improve the digital representation of reality.

Raghul Parthipan, Hannah M. Christensen, J. Scott Hosking et al.

The modelling of small-scale processes is a major source of error in climate models, hindering the accuracy of low-cost models which must approximate such processes through parameterization. Red noise is essential to many operational parameterization schemes, helping model temporal correlations. We show how to build on the successes of red noise by combining the known benefits of stochasticity with machine learning. This is done using a physically-informed recurrent neural network within a probabilistic framework. Our model is competitive and often superior to both a bespoke baseline and an existing probabilistic machine learning approach (GAN) when applied to the Lorenz 96 atmospheric simulation. This is due to its superior ability to model temporal patterns compared to standard first-order autoregressive schemes. It also generalises to unseen scenarios. We evaluate across a number of metrics from the literature, and also discuss the benefits of using the probabilistic metric of hold-out likelihood.

Martin S J Rogers, Maria Fox, Andrew Fleming et al.

Synthetic Aperture Radar (SAR) imagery is the primary data type used for sea ice mapping due to its spatio-temporal coverage and the ability to detect sea ice independent of cloud and lighting conditions. Automatic sea ice detection using SAR imagery remains problematic due to the presence of ambiguous signal and noise within the image. Conversely, ice and water are easily distinguishable using multispectral imagery (MSI), but in the polar regions the ocean's surface is often occluded by cloud or the sun may not appear above the horizon for many months. To address some of these limitations, this paper proposes a new tool trained using concurrent multispectral Visible and SAR imagery for sea Ice Detection (ViSual\_IceD). ViSual\_IceD is a convolution neural network (CNN) that builds on the classic U-Net architecture by containing two parallel encoder stages, enabling the fusion and concatenation of MSI and SAR imagery containing different spatial resolutions. The performance of ViSual\_IceD is compared with U-Net models trained using concatenated MSI and SAR imagery as well as models trained exclusively on MSI or SAR imagery. ViSual\_IceD outperforms the other networks, with a F1 score 1.60\% points higher than the next best network, and results indicate that ViSual\_IceD is selective in the image type it uses during image segmentation. Outputs from ViSual\_IceD are compared to sea ice concentration products derived from the AMSR2 Passive Microwave (PMW) sensor. Results highlight how ViSual\_IceD is a useful tool to use in conjunction with PMW data, particularly in coastal regions. As the spatial-temporal coverage of MSI and SAR imagery continues to increase, ViSual\_IceD provides a new opportunity for robust, accurate sea ice coverage detection in polar regions.

Raghul Parthipan, Mohit Anand, Hannah M. Christensen et al.

Machine learning (ML) has recently shown significant promise in modelling atmospheric systems, such as the weather. Many of these ML models are autoregressive, and error accumulation in their forecasts is a key problem. However, there is no clear definition of what `error accumulation' actually entails. In this paper, we propose a definition and an associated metric to measure it. Our definition distinguishes between errors which are due to model deficiencies, which we may hope to fix, and those due to the intrinsic properties of atmospheric systems (chaos, unobserved variables), which are not fixable. We illustrate the usefulness of this definition by proposing a simple regularization loss penalty inspired by it. This approach shows performance improvements (according to RMSE and spread/skill) in a selection of atmospheric systems, including the real-world weather prediction task.

Anna Vaughan, Stratis Markou, Will Tebbutt et al.

Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather prediction pipeline, but current approaches still rely on numerical weather prediction (NWP) systems, limiting forecast speed and accuracy. Here we demonstrate that a machine learning model can replace the entire operational NWP pipeline. Aardvark Weather, an end-to-end data-driven weather prediction system, ingests raw observations and outputs global gridded forecasts and local station forecasts. Further, it can be optimised end-to-end to maximise performance over quantities of interest. Global forecasts outperform an operational NWP baseline for multiple variables and lead times. Local station forecasts are skillful up to ten days lead time and achieve comparable and often lower errors than a post-processed global NWP baseline and a state-of-the-art end-to-end forecasting system with input from human forecasters. These forecasts are produced with a remarkably simple neural process model using just 8% of the input data and three orders of magnitude less compute than existing NWP and hybrid AI-NWP methods. We anticipate that Aardvark Weather will be the starting point for a new generation of end-to-end machine learning models for medium-range forecasting that will reduce computational costs by orders of magnitude and enable the rapid and cheap creation of bespoke models for users in a variety of fields, including for the developing world where state-of-the-art local models are not currently available.

Tom Dunstan, Oliver Strickson, Thusal Bennett et al.

Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at significantly reduced computational cost compared to traditional numerical weather prediction (NWP) systems. However, challenges remain in ensuring the physical consistency of MLWP outputs, particularly in deterministic settings. This study presents FastNet, a graph neural network (GNN)-based global prediction model, and investigates the impact of alternative loss function designs on improving the physical realism of its forecasts. We explore three key modifications to the standard mean squared error (MSE) loss: (1) a modified spherical harmonic (MSH) loss that penalises spectral amplitude errors to reduce blurring and enhance small-scale structure retention; (2) inclusion of horizontal gradient terms in the loss to suppress non-physical artefacts; and (3) an alternative wind representation that decouples speed and direction to better capture extreme wind events. Results show that while the MSH and gradient-based losses \textit{alone} may slightly degrade RMSE scores, when trained in combination the model exhibits very similar MSE performance to an MSE-trained model while at the same time significantly improving spectral fidelity and physical consistency. The alternative wind representation further improves wind speed accuracy and reduces directional bias. Collectively, these findings highlight the importance of loss function design as a mechanism for embedding domain knowledge into MLWP models and advancing their operational readiness.

Anna Vaughan, Will Tebbutt, J. Scott Hosking et al.

A new model is presented for multisite statistical downscaling of temperature and precipitation using convolutional conditional neural processes (convCNPs). ConvCNPs are a recently developed class of models that allow deep learning techniques to be applied to off-the-grid spatio-temporal data. This model has a substantial advantage over existing downscaling methods in that the trained model can be used to generate multisite predictions at an arbitrary set of locations, regardless of the availability of training data. The convCNP model is shown to outperform an ensemble of existing downscaling techniques over Europe for both temperature and precipitation taken from the VALUE intercomparison project. The model also outperforms an approach that uses Gaussian processes to interpolate single-site downscaling models at unseen locations. Importantly, substantial improvement is seen in the representation of extreme precipitation events. These results indicate that the convCNP is a robust downscaling model suitable for generating localised projections for use in climate impact studies, and motivates further research into applications of deep learning techniques in statistical downscaling.

Ushnish Sengupta, Matt Amos, J. Scott Hosking et al.

Ensembles of geophysical models improve projection accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware projections without sacrificing interpretability. Applied to the prediction of total column ozone from an ensemble of 15 chemistry-climate models, we find that the Bayesian neural network ensemble (BayNNE) outperforms existing ensembling methods, achieving a 49.4% reduction in RMSE for temporal extrapolation, and a 67.4% reduction in RMSE for polar data voids, compared to a weighted mean. Uncertainty is also well-characterized, with 90.6% of the data points in our extrapolation validation dataset lying within 2 standard deviations and 98.5% within 3 standard deviations.

Wessel P. Bruinsma, Eric Perim, Will Tebbutt et al.

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is their computational scaling $O(n^3 p^3)$, which is cubic in the number of both inputs $n$ (e.g., time points or locations) and outputs $p$. For this reason, a popular class of MOGPs assumes that the data live around a low-dimensional linear subspace, reducing the complexity to $O(n^3 m^3)$. However, this cost is still cubic in the dimensionality of the subspace $m$, which is still prohibitively expensive for many applications. We propose the use of a sufficient statistic of the data to accelerate inference and learning in MOGPs with orthogonal bases. The method achieves linear scaling in $m$ in practice, allowing these models to scale to large $m$ without sacrificing significant expressivity or requiring approximation. This advance opens up a wide range of real-world tasks and can be combined with existing GP approximations in a plug-and-play way. We demonstrate the efficacy of the method on various synthetic and real-world data sets.