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This article describes a memory efficient method for solving large-scale optimization problems that arise when planning scanning-beam lithography processes. These processes require the identification of an exposure pattern that minimizes the difference between a desired and predicted output image, subject to constraints. The number of free variables is equal to the number of pixels, which can be on the order of millions or billions in practical applications. The proposed method splits the problem domain into a number of smaller overlapping subdomains with constrained boundary conditions, which are then solved sequentially using a constrained gradient search method (L-BFGS-B). Computational time is reduced by exploiting natural sparsity in the problem and employing the fast Fourier transform for efficient gradient calculation. When it comes to the trade-off between memory usage and computational time we can make a different trade-off compared to previous methods, where the required memory is reduced by approximately the number of subdomains at the cost of more computations. In an example problem with 30 million variables, the proposed method reduces memory requirements by 67% but increases computation time by 27%. Variations of the proposed method are expected to find applications in the planning of processes such as scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition, for example.

The role of non-pharmaceutical interventions (NPIs) on the spread of SARS-CoV-2 has drawn significant attention, both scientific and political. Particularly, an article by the Imperial College COVID-19 Response Team (ICCRT), published online in Nature on June 8, 2020, evaluates the efficiency of 5 NPIs. Based on mortality data up to early May, it concludes that only one of the interventions, lockdown, has been efficient in 10 out of 11 studied European countries.We show, via simulations using the ICCRT model code, that conclusions regarding the effectiveness of individual NPIs are not justified. Our analysis focuses on the 11th country, Sweden, an outlier in that no lockdown was effectuated. The new simulations show that estimated NPI efficiencies across all 11 countries change drastically unless the model is adapted to give the Swedish data special treatment. While stated otherwise in the Nature article, such adaptation has been done in the model code reproducing its results: An ungrounded country-specific parameter said to have been introduced in all 11 countries, is in the code only activated for Sweden. This parameter de facto provides a new NPI category, only present in Sweden, and with an impact comparable to that of a lockdown.While the considered NPIs have unarguably contributed to reduce virus spread, our analysis reveals that their individual efficiency cannot be reliably quantified by the ICCRT model, provided mortality data up to early May.

IntroductionA series of modelling reports that quantify the effect of non-pharmaceutical interventions (NPIs) on the spread of the SARS-CoV-2 virus have been made available prior to external scientific peer-review. The aim of this study was to investigate the method used by the Imperial College COVID-19 Research Team (ICCRT) for estimation of NPI effects from the system theoretical viewpoint of model identifiability.MethodsAn input-sensitivity analysis was performed by running the original software code of the systems model that was devised to estimate the impact of NPIs on the reproduction number of the SARS-CoV-2 infection and presented online by ICCRT in Report 13 on March 30 2020. An empirical investigation was complemented by an analysis of practical parameter identifiability, using an estimation theoretical framework.ResultsDespite being simplistic with few free parameters, the system model was found to suffer from severe input sensitivities. Our analysis indicated that the model lacks practical parameter identifiability from data. The analysis also showed that this limitation is fundamental, and not something readily resolved should the model be driven with data of higher reliability.DiscussionReports based on system models have been instrumental to policymaking during the SARS-CoV-2 pandemic. With much at stake during all phases of a pandemic, we conclude that it is crucial to thoroughly scrutinise any SARS-CoV-2 effect analysis or prediction model prior to considering its use as decision support in policymaking. The enclosed example illustrates what such a review might reveal.

Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing $d_0$ is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not alter this parameter. In this paper, we consider the more general problem of jointly reconstructing the strain and $d_0$ fields. A method for solving this inherently non-linear problem is presented that ensures the estimated strain field satisfies equilibrium and can include knowledge of boundary conditions. This method is tested on a simulated data set with realistic noise levels, demonstrating that it is possible to jointly reconstruct $d_0$ and the strain field., Journal article, 14 pages, 5 figures

During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. This is combined with a stochastic line search relying upon fulfilment of the Wolfe condition in a backtracking manner, where the step length is adaptively modified with respect to the optimisation progress. We support our new algorithm by providing several theoretical results guaranteeing its performance. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods., arXiv admin note: substantial text overlap with arXiv:1802.04310

This paper deals with modelling and reconstruction of strain fields, relying upon data generated from neutron Bragg-edge measurements. We propose a probabilistic approach in which the strain field is modelled as a Gaussian process, assigned a covariance structure customised by incorporation of the so-called equilibrium constraints. The computational complexity is significantly reduced by utilising an approximation scheme well suited for the problem. We illustrate the method on simulations and real data. The results indicate a high potential and can hopefully inspire the concept of probabilistic modelling to be used within other tomographic applications as well.

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from measured data. In contrast to other established methods, this comes with the advantage of not requiring any manual parameter tuning, which usually arises in classical regularization strategies. Our method uses a basis function expansion technique for the Gaussian process which significantly reduces the computational complexity and avoids the need for numerical integration. The approach also allows for reformulation of come classical regularization methods as Laplacian and Tikhonov regularization as Gaussian process regression, and hence provides an efficient algorithm and principled means for their parameter tuning. Results from simulated and real data indicate that this approach is less sensitive to streak artifacts as compared to the commonly used method of filtered backprojection.