a b s t r a c tSparse grids allow one to employ grid-based discretization methods in data-driven problems. We present an extension of the classical sparse grid approach that allows us to tackle highdimensional problems by spatially adaptive refinement, modified ansatz functions, and efficient regularization techniques. The competitiveness of this method is shown for typical benchmark problems with up to 166 dimensions for classification in data mining, pointing out properties of sparse grids in this context. To gain insight into the adaptive refinement and to examine the scope for further improvements, the approximation of non-smooth indicator functions with adaptive sparse grids has been studied as a model problem. As an example for an improved adaptive grid refinement, we present results for an edge-detection strategy.

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Objective Rapid testing is paramount during a pandemic to prevent continued viral spread and excess morbidity and mortality. This study investigates whether testing strategies based on sample pooling can increase the speed and throughput of screening for SARS-CoV-2, especially in resource-limited settings. Methods In a mathematical modelling approach conducted in May 2020, six different testing strategies were simulated based on key input parameters such as infection rate, test characteristics, population size, and testing capacity. The situations in five countries were simulated, reflecting a broad variety of population sizes and testing capacities. The primary study outcome measurements were time and number of tests required, number of cases identified, and number of false positives. Findings The performance of all tested methods depends on the input parameters, i.e. the specific circumstances of a screening campaign. To screen one tenth of each country’s population at an infection rate of 1%, realistic optimised testing strategies enable such a campaign to be completed in ca. 29 days in the US, 71 in the UK, 25 in Singapore, 17 in Italy, and 10 in Germany. This is ca. eight times faster compared to individual testing. When infection rates are lower, or when employing an optimal, yet more complex pooling method, the gains are more pronounced. Pool-based approaches also reduce the number of false positive diagnoses by a factor of up to 100. Conclusions The results of this study provide a rationale for adoption of pool-based testing strategies to increase speed and throughput of testing for SARS-CoV-2, hence saving time and resources compared with individual testing.