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Data-driven surrogate models have shown immense potential as quick, inexpensive approximations to complex numerical and experimental modelling tasks. However, most surrogate models characterising physical systems do not quantify their uncertainty, rendering their predictions unreliable, and needing further validation. Though Bayesian approximations offer some solace in estimating the error associated with these models, they cannot provide they cannot provide guarantees, and the quality of their inferences depends on the availability of prior information and good approximations to posteriors for complex problems. This is particularly pertinent to multi-variable or spatio-temporal problems. Our work constructs and formalises a conformal prediction framework that satisfies marginal coverage for spatio-temporal predictions in a model-agnostic manner, requiring near-zero computational costs. The paper provides an extensive empirical study of the application of the framework to ascertain valid error bars that provide guaranteed coverage across the surrogate model's domain of operation. The application scope of our work extends across a large range of spatio-temporal models, ranging from solving partial differential equations to weather forecasting. Through the applications, the paper looks at providing statistically valid error bars for deterministic models, as well as crafting guarantees to the error bars of probabilistic models. The paper concludes with a viable conformal prediction formalisation that provides guaranteed coverage of the surrogate model, regardless of model architecture, and its training regime and is unbothered by the curse of dimensionality.

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.

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.

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 synchronisation overhead in this setting. In this paper, 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.

The SETI Ellipsoid is a strategy for technosignature candidate selection which assumes that extraterrestrial civilizations who have observed a galactic-scale event -- such as supernova 1987A -- may use it as a Schelling point to broadcast synchronized signals indicating their presence. Continuous wide-field surveys of the sky offer a powerful new opportunity to look for these signals, compensating for the uncertainty in their estimated time of arrival. We explore sources in the TESS continuous viewing zone, which corresponds to 5% of all TESS data, observed during the first three years of the mission. Using improved 3D locations for stars from Gaia Early Data Release 3, we identified 32 SN 1987A SETI Ellipsoid targets in the TESS continuous viewing zone with uncertainties better than 0.5 ly. We examined the TESS light curves of these stars during the Ellipsoid crossing event and found no anomalous signatures. We discuss ways to expand this methodology to other surveys, more targets, and different potential signal types., Comment: 17 pages, 6 figures, AJ published

An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected size is a time-dependent quantity and so enables the identification of nodes who are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalises the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks., Comment: 16 pages, 5 figures

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.

The SETI Ellipsoid is a geometric method for prioritizing technosignature observations based on the strategy of receiving signals synchronized to conspicuous astronomical events. Precise distances to nearby stars from Gaia makes constraining Ellipsoid crossing times possible. Here we explore the utility of using the Gaia Catalog of Nearby Stars to select targets on the SN 1987A SETI Ellipsoid, as well the Ellipsoids defined by 278 classical novae. Less than 8% of stars within the 100 pc sample are inside the SN 1987A SETI Ellipsoid, meaning the vast majority of nearby stars are still viable targets for monitoring over time. We find an average of 734 stars per year within the 100 pc volume will intersect the Ellipsoid from SN 1987A, with ~10% of those having distance uncertainties from Gaia better than 0.1 lyr., Comment: 11 pages, 7 figures, Submitted to the AAS Journals

Magnetic activity in stars manifests as dark spots on their surfaces that modulate the brightness observed by telescopes. These light curves contain important information on stellar rotation. However, the accurate estimation of rotation periods is computationally expensive due to scarce ground truth information, noisy data, and large parameter spaces that lead to degenerate solutions. We harness the power of deep learning and successfully apply Convolutional Neural Networks to regress stellar rotation periods from Kepler light curves. Geometry-preserving time-series to image transformations of the light curves serve as inputs to a ResNet-18 based architecture which is trained through transfer learning. The McQuillan catalog of published rotation periods is used as ansatz to groundtruth. We benchmark the performance of our method against a random forest regressor, a 1D CNN, and the Auto-Correlation Function (ACF) - the current standard to estimate rotation periods. Despite limiting our input to fewer data points (1k), our model yields more accurate results and runs 350 times faster than ACF runs on the same number of data points and 10,000 times faster than ACF runs on 65k data points. With only minimal feature engineering our approach has impressive accuracy, motivating the application of deep learning to regress stellar parameters on an even larger scale, Comment: Accepted for the Machine Learning and the Physical Sciences Workshop, NeurIPS 2020

Our understanding of the Universe has profited from deliberate, targeted studies of known phenomena, as well as from serendipitous, unexpected discoveries, such as the discovery of a complex variability pattern in the direction of KIC 8462852 (Boyajian's star). Upcoming surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), will explore the parameter space of astrophysical transients at all time scales, and offer the opportunity to discover even more extreme examples of unexpected phenomena. We investigate strategies to identify novel objects and to contextualize them within large time-series data sets in order to facilitate the discovery of new classes of objects, as well as the physical interpretation of their anomalous nature. We develop a method that combines tree-based and manifold-learning algorithms for anomaly detection in order to perform two tasks: 1) identify and rank anomalous objects in a time-domain dataset; and 2) group those anomalies according to their similarity in order to identify analogs. We achieve the latter by combining an anomaly score from a tree-based method with a dimensionality manifold-learning reduction strategy. Clustering in the reduced space allows for the successful identification of anomalies and analogs. We also assess the impact of pre-processing and feature engineering schemes and investigate the astrophysical nature of the objects that our models identify as anomalous by augmenting the Kepler data with Gaia color and luminosity information. We find that multiple models, used in combination, are a promising strategy to identify novel light curves and light curve families., Comment: 29 pages, 22 figures, accepted to MNRAS

Accurate and efficient tsunami modelling is essential for providing tsunami forecasts and hazard assessments. Volna-OP2 is a finite volume solver of the nonlinear shallow water equations and its capabilities of producing both faster than real time ensembles and high resolution inundation studies are presented here. The code is massively parallelised and can utilise various high performance computing architectures. When an earthquake is detected there is always some uncertainty on the source parameters. Generating a faster than real time ensemble for maximum wave heights which captures this uncertainty would be of great benefit to tsunami warning centres. The 2003 Boumerdes earthquake (Algeria) acts as a test case for showing Volna-OP2's ability at rapidly forecasting regional maximum wave heights. Drawing on various earthquake sources proposed in the literature and scaling the magnitudes to mimic uncertainty on the source, 20 separate earthquake realisations are simulated for 4 hours real time in 97s on two Nvidia V100 GPUs. Further a reduced ensemble of the Lisbon 1755 tsunami with an emphasis on the effects to the Irish coastline is presented. Where again various earthquake sources have been drawn from the literature and simulated on a regional scale. Finally, a pilot study which builds upon the reduced ensemble results investigates the inundation of a Lisbon tsunami on key sections of the Irish coastline. The results of this pilot study highlight that the inundation is constrained to low-lying areas with maximum run-up heights of $\approx 3.4m$ being found.

In the present era of large scale surveys, big data presents new challenges to the discovery process for anomalous data. Such data can be indicative of systematic errors, extreme (or rare) forms of known phenomena, or most interestingly, truly novel phenomena which exhibit as-of-yet unobserved behaviors. In this work we present an outlier scoring methodology to identify and characterize the most promising unusual sources to facilitate discoveries of such anomalous data. We have developed a data mining method based on k-Nearest Neighbor distance in feature space to efficiently identify the most anomalous lightcurves. We test variations of this method including using principal components of the feature space, removing select features, the effect of the choice of k, and scoring to subset samples. We evaluate the peformance of our scoring on known object classes and find that our scoring consistently scores rare (<1000) object classes higher than common classes. We have applied scoring to all long cadence lightcurves of quarters 1 to 17 of Kepler's prime mission and present outlier scores for all 2.8 million lightcurves for the roughly 200k objects., Comment: 14 pages, 11 figures, plus appendices, 4 supplemental tables hosted online at https://doi.org/10.7910/DVN/H5QXUL

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.

Advances in astronomy are often driven by serendipitous discoveries. As survey astronomy continues to grow, the size and complexity of astronomical databases will increase, and the ability of astronomers to manually scour data and make such discoveries decreases. In this work, we introduce a machine learning-based method to identify anomalies in large datasets to facilitate such discoveries, and apply this method to long cadence lightcurves from NASA's Kepler Mission. Our method clusters data based on density, identifying anomalies as data that lie outside of dense regions. This work serves as a proof-of-concept case study and we test our method on four quarters of the Kepler long cadence lightcurves. We use Kepler's most notorious anomaly, Boyajian's Star (KIC 8462852), as a rare `ground truth' for testing outlier identification to verify that objects of genuine scientific interest are included among the identified anomalies. We evaluate the method's ability to identify known anomalies by identifying unusual behavior in Boyajian's Star, we report the full list of identified anomalies for these quarters, and present a sample subset of identified outliers that includes unusual phenomena, objects that are rare in the Kepler field, and data artifacts. By identifying <4% of each quarter as outlying data, we demonstrate that this anomaly detection method can create a more targeted approach in searching for rare and novel phenomena., Comment: 21 pages, 10 figures, Submitted to MNRAS

In this paper we develop algorithms to solve generalized weighted Fermat-Torricelli problems with positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems.

The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov's accelerated gradient method, we present an effective numerical algorithm for solving these problems.