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Abstract We present GPSat; an open-source Python programming library for performing efficient interpolation of non-stationary satellite altimetry data, using scalable Gaussian process techniques. We use GPSat to generate complete maps of daily 50 km-gridded Arctic sea ice radar freeboard, and find that, relative to a previous interpolation scheme, GPSat offers a 504 × computational speedup, with less than 4 mm difference on the derived freeboards on average. We then demonstrate the scalability of GPSat through freeboard interpolation at 5 km resolution, and Sea-Level Anomalies (SLA) at the resolution of the altimeter footprint. Interpolated 5 km radar freeboards show strong agreement with airborne data (linear correlation of 0.66). Footprint-level SLA interpolation also shows improvements in predictive skill over linear regression. In this work, we suggest that GPSat could overcome the computational bottlenecks faced in many altimetry-based interpolation routines, and hence advance critical understanding of ocean and sea ice variability over short spatio-temporal scales.

The Sentinel-3A and Sentinel-3B satellites, launched in February 2016 and April 2018 respectively, build on the legacy of CryoSat-2 by providing high-resolution Ku-band radar altimetry data over the polar regions up to 81° North. The combination of synthetic aperture radar (SAR) mode altimetry (SRAL instrument) from Sentinel-3A and Sentinel-3B, and the Ocean and Land Colour Instrument (OLCI) imaging spectrometer, results in the creation of the first satellite platform that offers coincident optical imagery and SAR radar altimetry. We utilise this synergy between altimetry and imagery to demonstrate a novel application of deep learning to distinguish sea ice from leads in spring. We use SRAL classified leads as training input for pan-Arctic lead detection from OLCI imagery. This surface classification is an important step for estimating sea ice thickness and to predict future sea ice changes in the Arctic and Antarctic regions. We propose the use of Vision Transformers (ViT), an approach adapting the popular deep learning algorithm Transformer, for this task. Their effectiveness, in terms of both quantitative metric including accuracy and qualitative metric including model roll-out, on several entire OLCI images is demonstrated and we show improved skill compared to previous machine learning and empirical approaches. We show the potential for this method to provide lead fraction retrievals at improved accuracy and spatial resolution for sunlit periods before melt onset.

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier neural operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (Mean Squared Error in the normalised domain ${\approx}10^{-5}$ ). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations, and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e. cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

For a broad range of research and practical applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich relational data in digital social networks (the social graph). As global social networks (e.g., Facebook and Twitter) are very large, most approaches make use of distributed computing systems for this purpose. Distributing graph processing requires solving many difficult engineering problems, which has lead some researchers to look at single-machine solutions that are faster and easier to maintain. In this article, we present an approach for analyzing full social networks on a standard laptop, allowing for interactive exploration of the communities in the locality of a set of user specified query vertices. The key idea is that the aggregate actions of large numbers of users can be compressed into a data structure that encapsulates the edge weights between vertices in a derived graph. Local communities can be constructed by selecting vertices that are connected to the query vertices with high edge weights in the derived graph. This compression is robust to noise and allows for interactive queries of local communities in real-time, which we define to be less than the average human reaction time of 0.25s. We achieve single-machine real-time performance by compressing the neighborhood of each vertex using minhash signatures and facilitate rapid queries through Locality Sensitive Hashing. These techniques reduce query times from hours using industrial desktop machines operating on the full graph to milliseconds on standard laptops. Our method allows exploration of strongly associated regions (i.e., communities) of large graphs in real-time on a laptop. It has been deployed in software that is actively used by social network analysts and offers another channel for media owners to monetize their data, helping them to continue to provide free services that are valued by billions of people globally.