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 (Multi-layer perceptrons, U-Net, Fourier neural operator, 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.

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.

Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings. Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results. In this paper, we propose Tensor-Var, a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space. Moreover, our method provides a new perspective for solving 4D-Var in a linear way, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To handle large-scale problems, we propose a method to learn deep features using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving a 10- to 20-fold speed improvement.

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

The under-representation of cloud formation is a long-standing bias associated with climate simulations. Parameterisation schemes are required to capture cloud processes within current climate models but have known biases. We overcome these biases by embedding a Multi-Output Gaussian Process (MOGP) trained on high resolution Unified Model simulations to represent the variability of temperature and specific humidity within a climate model. A trained MOGP 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 MOGP. Ten-year predictions are generated for both control and ML-hybrid models. The hybrid model reduces the global precipitation bias by 18\% and over the tropics by 22\%. To further understand the drivers of these improvements, physical quantities of interest are explored, such as the distribution of lifted index values and the alteration of the Hadley cell. The control and hybrid set-ups are also run in a plus 4K sea-surface temperature experiment to explore the effects of the approach on patterns relating to cloud cover and precipitation in a warmed climate setting.

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. Hybrid machine learning techniques can improve the representation of precipitation biases, reducing global error by up to 17% and over the tropics by up to 20%, according to results from a Multi-Output Gaussian Process coupled with a simplified Atmospheric General Circulation Model named SPEEDY.

Neural weather models have shown immense potential as inexpensive and accurate alternatives to physics-based models. However, most models trained to perform weather forecasting do not quantify the uncertainty associated with their forecasts. This limits the trust in the model and the usefulness of the forecasts. In this work we construct and formalise a conformal prediction framework as a post-processing method for estimating this uncertainty. The method is model-agnostic and gives calibrated error bounds for all variables, lead times and spatial locations. No modifications are required to the model and the computational cost is negligible compared to model training. We demonstrate the usefulness of the conformal prediction framework on a limited area neural weather model for the Nordic region. We further explore the advantages of the framework for deterministic and probabilistic models.

By bringing together a large group of participants with diverse skillsets, hackathons aim to make good headway into a particular research topic over a short period of time. This collaborative approach supports relationship building, cross team working and the development of technical skills across different areas.image

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 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.

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.

Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We propose to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators. We show, using both theory and numerical experiments, that our approach can lead to significant improvements in accuracy when the integrand is expensive and smooth, and when the dimensionality is small or moderate. We conclude the paper with a case study illustrating the potential impact of our method in landslide-generated tsunami modelling, where the cost of each integrand evaluation is typically too large for operational settings.

High resolution global climate simulations are computationally intractable due to the integration over long time scales. Therefore coarse spatial resolution models are used. One of the known failings of current climate simulations is the underrepresentation of cloud formation, which is largely due to the disparity in the spatial scale of the model and the underlying cloud generating physical processes. In this work emphasis has been placed on fusing an emulator with a climate model so as to embed high resolution variability into a coarse resolution climate model - with the aim of improving the representation of convective cloud formation. A multi-output Gaussian Process (MOGP) is trained on high resolution Unified Model (UM) runs to predict the variability on the temperature and specific humidity fields. A proof of concept study has been carried out where the trained MOGP model is then coupled in-situ with a simplified Atmospheric General Circulation Model (AGCM) named SPEEDY. The mean profiles of the SPEEDY model are perturbed at each timestep according to the predicted high resolution informed variability. The climate statistics from the fused model are then compared to the pure model run. Improvements in the precipitation, outgoing longwave and shortwave radiation patterns are observed.

Abstract. 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.

Local bathymetry and onshore features can have a substantial effect on the spatial variability of the hazard from an incoming tsunami. In a warning context, being able to provide localized tsunami forecasts at strategic locations would therefore help mitigate the damage. Despite the recent advancements in computing powers and the development of highly efficient tsunami codes, capturing this local variability can oftentimes be infeasible in a warning setting. Traditional high-resolution simulations which can capture these localized effects are often too costly to run "on-the-fly." Alternative approaches that capture the localized response to an incoming tsunami, which are based upon using the maximum wave heights from a computationally cheap regional forecast, are developed here. These alternative approaches are envisaged to aid in a warning center's ability at providing extremely rapid localized forecasts. The approaches focus upon two different methods: transfer functions and machine learning techniques. The transfer function is based upon a recent extension to the established Green's Law. The extended version introduces local amplification parameters, with the aim of capturing the neglected localized effects. An automated approach which optimizes for these local amplification parameters is outlined and the performance of the transfer function is explored. A machine learning model is also trained and used to predict the localized tsunami hazard. Its performance is compared to the extended Green's Law approach for a site along the French coast. These developed methods showcase promising techniques that a tsunami warning center could use to provide high-resolution warnings.

Tsunamis are unpredictable events and catastrophic in their potential for destruction of human lives and economy. The unpredictability of their occurrence poses a challenge to the tsunami community, as it is difficult to obtain from the tsunamigenic records estimates of recurrence rates and severity. Accurate and efficient mathematical/computational modeling is thus called upon to provide tsunami forecasts and hazard assessments. Compounding this challenge for warning centres is the physical nature of tsunamis, which can travel at extremely high speeds in the open ocean or be generated close to the shoreline. Thus, tsunami forecasts must be not only accurate but also delivered under severe time constraints. In the immediate aftermath of a tsunamigenic earthquake event, there are uncertainties in the source such as location, rupture geometry, depth, magnitude. Ideally, these uncertainties should be represented in a tsunami warning. However in practice, quantifying the uncertainties in the hazard intensity ( i.e., maximum tsunami amplitude) due to the uncertainties in the source is not feasible, since it requires a large number of high resolution simulations. We approximate the functionally complex and computationally expensive high resolution tsunami simulations with a simple and cheap statistical emulator. A workflow integrating the entire chain of components from the tsunami source to quantification of hazard uncertainties is developed here - quantification of uncertainties in tsunamigenic earthquake sources, high resolution simulation of tsunami scenarios using the GPU version of Volna-OP2 on a non-uniform mesh for an ensemble of sources, construction of an emulator using the simulations as training data, and prediction of hazard intensities with associated uncertainties using the emulator. Thus, using the massively parallelized finite volume tsunami code Volna-OP2 as the heart of the workflow, we use statistical emulation to compute uncertainties in hazard intensity at locations of interest. Such an integration also balances the trade-off between computationally expensive simulations and desired accuracy of uncertainties, within given time constraints. The developed workflow is fully generic and independent of the source (1945 Makran earthquake) studied here.

In the framework of operational conditions, the real time coastal modeling in near field is challenging to obtain accurate and reliable tsunami warning products for flooding hazard. Two main approaches are usually developed to generate maps of forecasting inundation and impacts for planning community response. One produces coastal predictions with run-up computation by solving numerically high-resolution forecast models in real time, taking into account all local effects. However, these runs depend on the availability of fine bathymetry/topography grids along the shore and are too time consuming in near field and operational context. The second approach is based on early prediction tools of the coastal wave amplitude calculated from empirical laws or transfer functions derived from these laws. Such tools are suitable in near field context (almost ten times faster than the high-resolution runs), but all local effects are not well taken into account and the assessment of run-up is missing. The linear approximations of coastal tsunami heights are provided very quickly, with global and conservative estimates.Within the French Tsunami Warning Center (CENALT), a forecast method based on coastal amplification laws is being implemented. This fast prediction tool provides a coastal tsunami height distribution, calculated from the numerical simulation of the deep ocean tsunami amplitude and using a transfer function derived from the Green’s law. The method involves maps of regionalized values of the empirical correction factor function of the coastal configuration, as a way to amplify or attenuate specific local geometries. Due to a lack of tsunami observations in the NEAM basin, coastal amplification parameters are defined by trial and error regarding high resolution nested grids simulations on the basis of a set of historical and synthetic sources. A method to optimize these local amplification factors by minimizing a cost function is being developed at UCD. Comparisons are shown for several French coastal sites.The local tsunami wave heights modeled from the extended Green’s law present a good agreement with the time-consuming high resolution models. The linear approximation is obtained within 1 min and provides estimates within a factor of two in amplitude. Although the resonance effects in harbors and bays are not reproduced and the horizontal inundation calculation needs to be studied further, this method is well suited for an early first estimate of the coastal tsunami threat forecast.

Tsunamis are infrequent events that have the potential to be extremely destructive. The last major tsunami to effect the Irish coastline was the Lisbon 1755 event. That event acts as a candidate worst case scenario for hazard assessment and the impacts on the Irish Coastline are presented here. As there is no general consensus on the 1755 earthquake source, multiple sources highlighted in the literature are investigated. These sources are used to generate the initial conditions and the resultant tsunami waves are simulated with the massively parallelised Volna-OP2 finite volume tsunami code. The hazard associated with the event is captured on three gradated levels. A reduced faster than real time tsunami ensemble is produced for the North-East Atlantic on a regional level in 93 s using two Nvidia V100 GPUs. By identifying the most vulnerable sections of the Irish coastline from this regional forecast, some locally refined simulations are further carried out in a faster than real time setting. As arrival times on the coastline can be on theO(mins), these faster than real time reduced ensembles are of great benefit for tsunami warning. Volna-OP2's capabilities in this respect are clearly demonstrated here. Finally, high resolution inundation simulations, which build upon the ensemble results, are carried out. To date this study provides the best estimate of assessing the hazard associated with a Lisbon-type tsunami event for the Irish coastline. The results of the inundation mapping highlight that along the vulnerable sections of coastline, inundation is constrained to low-lying areas with maximum run-up heights of 3.4 m being found.

The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences. It is the first time that the errors of a tsunami code have been assessed in this manner. To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.