Large supercomputing facilities are critical to research in many areas that impact on decisions such as how to address the current climate emergency. For example, climate modelling, renewable energy facility design and new battery technologies. However, these systems themselves are a source of large amounts of emissions due to the embodied emissions associated with their construction, transport, and decommissioning; and the power consumption associated with running the facility. Recently, the UK National Supercomputing Service, ARCHER2, has been analysing the impact of the facility in terms of energy and emissions. Based on this work, we have made changes to the operation of the service that give a cumulative saving of more than 20% in power draw of the computational resources with all application benchmarks showing reduced power to solution. In this paper, we describe our analysis and the changes made to the operation of the service to improve its energy efficiency, and thereby reduce its climate impacts.
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Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for specifying Gaussian fields on metric graphs, the Whittle-Mat\'ern fields are well-defined for any compact metric graph and can provide Gaussian processes with differentiable sample paths. We derive the main statistical properties of the model class, particularly the consistency and asymptotic normality of maximum likelihood estimators of model parameters and the necessary and sufficient conditions for asymptotic optimality properties of linear prediction based on the model with misspecified parameters. The covariance function of the Whittle-Mat\'ern fields is generally unavailable in closed form, and they have therefore been challenging to use for statistical inference. However, we show that for specific values of the fractional exponent, when the fields have Markov properties, likelihood-based inference and spatial prediction can be performed exactly and computationally efficiently. This facilitates using the Whittle-Mat\'ern fields in statistical applications involving big datasets without the need for any approximations. The methods are illustrated via an application to modeling of traffic data, where allowing for differentiable processes dramatically improves the results.
The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot and its surroundings have to be executed along with other nominal tasks. In such cases, it is also important to prioritize the former over the latter. In this paper, we formalize the definition of extended set-based tasks, i.e., tasks which can be executed by rendering subsets of the task space asymptotically stable or forward invariant. We propose a mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present and analyze an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations and experiments with robotic manipulators.
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof. This simulator is efficient in that it exploits of the low dimension of the invariant manifold, and takes time steps of size dependent on the regularity of the effective process, and therefore typically much larger than that of the original simulator, which had to resolve the fast modes. The algorithm and the estimation can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.
Forced alignment systems automatically determine boundaries between segments in speech data, given an orthographic transcription. These tools are commonplace in phonetics to facilitate the use of speech data that would be infeasible to manually transcribe and segment. In the present paper, we describe a new neural network-based forced alignment system, the Mason-Alberta Phonetic Segmenter (MAPS). The MAPS aligner serves as a testbed for two possible improvements we pursue for forced alignment systems. The first is treating the acoustic model in a forced aligner as a tagging task, rather than a classification task, motivated by the common understanding that segments in speech are not truly discrete and commonly overlap. The second is an interpolation technique to allow boundaries more precise than the common 10 ms limit in modern forced alignment systems. We compare configurations of our system to a state-of-the-art system, the Montreal Forced Aligner. The tagging approach did not generally yield improved results over the Montreal Forced Aligner. However, a system with the interpolation technique had a 27.92% increase relative to the Montreal Forced Aligner in the amount of boundaries within 10 ms of the target on the test set. We also reflect on the task and training process for acoustic modeling in forced alignment, highlighting how the output targets for these models do not match phoneticians' conception of similarity between phones and that reconciliation of this tension may require rethinking the task and output targets or how speech itself should be segmented.
To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best among alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programmed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it! Despite their simplicity, mathematical tractability made models like the voter model (VM) and the local majority rule model (MR) useful to describe in simple terms such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbours in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, to reduce the cognitive load. Our analysis in grounded on the introduction of a model that generalises the two existing VM and MR models, showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show that another speed-accuracy trade-off is regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy
Recalling the most relevant visual memories for localisation or understanding a priori the likely outcome of localisation effort against a particular visual memory is useful for efficient and robust visual navigation. Solutions to this problem should be divorced from performance appraisal against ground truth - as this is not available at run-time - and should ideally be based on generalisable environmental observations. For this, we propose applying the recently developed Visual DNA as a highly scalable tool for comparing datasets of images - in this work, sequences of map and live experiences. In the case of localisation, important dataset differences impacting performance are modes of appearance change, including weather, lighting, and season. Specifically, for any deep architecture which is used for place recognition by matching feature volumes at a particular layer, we use distribution measures to compare neuron-wise activation statistics between live images and multiple previously recorded past experiences, with a potentially large seasonal (winter/summer) or time of day (day/night) shift. We find that differences in these statistics correlate to performance when localising using a past experience with the same appearance gap. We validate our approach over the Nordland cross-season dataset as well as data from Oxford's University Parks with lighting and mild seasonal change, showing excellent ability of our system to rank actual localisation performance across candidate experiences.
Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity analysis methods can effectively process such complexities. Moreover, the sensitivity analysis field as a whole pays limited attention to the nature of interaction effects, whose understanding can prove to be critical for the design of safe and reliable systems. In this paper, we introduce and extensively test a simple binning approach for computing sensitivity indices and demonstrate how complementing it with the smart visualization method, simulation decomposition (SimDec), can permit important insights into the behavior of complex engineering models. The simple binning approach computes first-, second-order effects, and a combined sensitivity index, and is considerably more computationally efficient than Sobol' indices. The totality of the sensitivity analysis framework provides an efficient and intuitive way to analyze the behavior of complex systems containing interactions and dependencies.
Differential geometric approaches are ubiquitous in several fields of mathematics, physics and engineering, and their discretizations enable the development of network-based mathematical and computational frameworks, which are essential for large-scale data science. The Forman-Ricci curvature (FRC) - a statistical measure based on Riemannian geometry and designed for networks - is known for its high capacity for extracting geometric information from complex networks. However, extracting information from dense networks is still challenging due to the combinatorial explosion of high-order network structures. Motivated by this challenge we sought a set-theoretic representation theory for high-order network cells and FRC, as well as their associated concepts and properties, which together provide an alternative and efficient formulation for computing high-order FRC in complex networks. We provide a pseudo-code, a software implementation coined FastForman, as well as a benchmark comparison with alternative implementations. Crucially, our representation theory reveals previous computational bottlenecks and also accelerates the computation of FRC. As a consequence, our findings open new research possibilities in complex systems where higher-order geometric computations are required.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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