Daniel Giles

Data-driven surrogate models offer fast, inexpensive approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide uncertainty estimates, they offer no statistical guarantees and struggle with high-dimensional spatio-temporal problems due to computational costs and dependence on prior specification. We present a conformal prediction (CP) framework that provides statistically guaranteed marginal coverage for surrogate models in a model-agnostic manner with near-zero computational cost. Our approach handles high-dimensional spatio-temporal outputs by performing cell-wise calibration while preserving the tensorial structure of predictions. Through extensive empirical evaluation across diverse applications—including partial differential equations, magnetohydrodynamics, weather forecasting, and fusion diagnostics—we demonstrate that CP achieves empirical coverage with valid error bars regardless of model architecture (MLP, U-Net, FNO, ViT, GNN), training regime, or output dimensionality (spanning 32 to over 20 million dimensions). We evaluate three nonconformity scores (conformalised quantile regression, absolute error residual, and standard deviation) for both deterministic and probabilistic models, showing that guaranteed coverage holds even for out-of-distribution predictions where models are deployed on physics regimes different from their training data. Calibration requires only seconds to minutes on standard hardware, with prediction set construction incurring negligible computational overhead. The framework enables rigorous validation of pre-trained surrogate models for downstream applications without retraining, providing actionable uncertainty quantification for decision-making in scientific domains. While CP provides marginal rather than conditional coverage and assumes exchangeability between calibration and test data—limitations we demonstrate empirically through sensitivity analyses—our method circumvents the curse of dimensionality inherent in traditional uncertainty quantification approaches, offering a practical tool for the trustworthy deployment of machine learning in the physical sciences.

An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected cascade size is a time-dependent quantity and so enables the identification of nodes that are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalizes the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks. Published by the American Physical Society 2025

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes; yet, existing approaches suffer from synchronization overhead in this setting. In this article, we exploit the formulation of data assimilation as a Bayesian inference problem and apply a message-passing algorithm to solve the spatial inference problem. Since message passing is inherently based on local computations, this approach lends itself to parallel and distributed computation. In combination with a GPU-accelerated implementation, we can scale the algorithm to very large grid sizes while retaining good accuracy and compute and memory requirements.

Parameterisation schemes within General Circulation Models are required to capture cloud processes and precipitation formation but exhibit long-standing known biases. Here, we develop a hybrid approach that tackles these biases by embedding a Multi-Output Gaussian Process trained to predict high resolution variability within each climate model grid box. The trained multi-output Gaussian Process model is coupled in-situ with a simplified Atmospheric General Circulation Model named SPEEDY. The temperature and specific humidity profiles of SPEEDY are perturbed at fixed intervals according to the variability predicted from the Gaussian Process. Ten-year predictions are generated for both control and machine learning hybrid models. The hybrid model reduces the global precipitation area-weighted root-mean squared error by up to 17% and over the tropics by up to 20%. Hybrid techniques have been known to introduce non-physical states therefore physical quantities are explored to ensure that climatic drift is not observed. Furthermore, to understand the drivers of the precipitation improvements the changes to thermodynamic profiles and the distribution of lifted index values are investigated.

We explore instances of unusual long-wave activity of meteorological origin along the coastal waters of north-west Europe during the summer of 2022. These events include meteorological tsunamis, i.e. waves in the tsunami frequency band originated by sharp atmospheric pressure variations and amplified by multiple resonant effects, and wind-generated infragravity waves which can trigger local seiches in enclosed basins and harboursAnomalous "tidal surges" were observed on 18 June 2022 in Wales, followed by similar occurrences in Ireland, France, and Spain. Additionally, several anomalous long-wave events were reported in south England and Wales on the morning of 19 July 2022. Our investigation involved analysing surface and high-altitude air pressure fields, as well as sea level oscillations for both days.We determine that the events on 18 June were a series of meteorological tsunamis, spreading across several western European countries and initiated by localised pressure disturbances originating within a low-pressure system over the North Atlantic Ocean. A local examination of the southern coast of Ireland suggests that Proudman resonance played a key role in amplifying the meteotsunami as it travelled eastward in the afternoon of 18 June. Similarly, our analysis of the events on 19 July indicates that the tidal surge observed in the UK and anomalous signals recorded in Ireland and France were likely instances of seiching triggered by infragravity waves. We conducted numerical simulations of the 18 June event using Volna-OP2, which solves the non-linear shallow water equations employing a finite volume discretisation technique. We also examined the influence of atmospheric wave velocity on the amplification of sea surface elevation.

Digital twins of physical and human systems informed by real-time data are becoming ubiquitous across weather forecasting, disaster preparedness, and urban planning, but researchers lack the tools to run these models effectively and efficiently, limiting progress. One of the current challenges is to assimilate observations in highly non-linear dynamical systems, as the practical need is often to detect abrupt changes. We have developed a software platform to improve the use of real-time data in non-linear system representations where non-Gaussianity limits the applicability of data assimilation algorithms such as the ensemble Kalman filter and variational methods. Particle-filter-based data assimilation algorithms have been implemented within a user-friendly open-source software platform in Julia – ParticleDA.jl. To ensure the applicability of the developed platform in realistic scenarios, emphasis has been placed on numerical efficiency and scalability on high-performance computing systems. Furthermore, the platform has been developed to be forward-model agnostic, ensuring that it is applicable to a wide range of modelling settings, for instance unstructured and non-uniform meshes in the spatial domain or even state spaces that are not spatially organized. Applications to tsunami and numerical weather prediction demonstrate the computational benefits and ease of using the high-level Julia interface with the package to perform filtering in a variety of complex models.

We investigate occurrences of anomalous tidal activity in coastal waters of north-west Europe during Summer 2022. Sightings of an anomalous “tidal surge” occurred on 18 June 2022 in Wales, followed by similar observations in Ireland, France, and Spain. Several anomalous long-wave events were also reported in south England and Wales in the morning of 19 July 2022. We analyzed surface and high-altitude air pressure fields, and sea level oscillations for both days. Our detailed analysis reveals that the 18 June events were a series of meteotsunamis, propagating over several countries in Western Europe and triggered by localized pressure perturbations, originating within a low-pressure area over the North Atlantic Ocean. A local analysis of the southern coast of Ireland suggests that Proudman resonance was the determinant mechanism that amplified the meteotsunami traveling eastward in the afternoon of 18 June. A similar analysis of the 19 July events suggests that the tidal surge reported in the UK and anomalous signals recorded in Ireland and France were episodes of seiching triggered by infragravity waves, resonated subharmonically by wind waves. Numerical simulations of the 18 June event were performed with Volna-OP2, which solves the non-linear shallow water equations using a finite volume discretization. The influence of the atmospheric wave velocity on the amplification of the sea surface elevation is analyzed.

Digital twins of physical and human systems informed by real-time data, are becoming ubiquitous across weather forecasting, disaster preparedness, and urban planning, but researchers lack the tools to run these models effectively and efficiently, limiting progress. One of the current challenges is to assimilate observations in highly nonlinear dynamical systems, as the practical need is often to detect abrupt changes. We developed a software platform to improve the use of real-time data in highly nonlinear system representations where non-Gaussianity prevents the use of more standard Data Assimilation. Optimal Particle filtering data assimilation (DA) techniques have been implemented within an user-friendly open source software platform in Julia – ParticleDA.jl. To ensure the applicability of the developed platform in realistic scenarios, emphasis has been placed on numerical efficiency, scalability and optimisation for high performance computing frameworks. Furthermore, the platform has been developed to be forward model agnostic, ensuring that it is applicable to a wide range of modelling settings, for instance unstructured and non-uniform meshes in the spatial domain or even state spaces that are not spatially organised. Applications to tsunami and numerical weather prediction demonstrate the computational benefits in terms of lower errors, lower computational costs (due to ensemble size and the algorithm's overheads being minimised) and versatility thanks to flexible I/O in a high level language Julia.