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Continue bose-einsteincondensatie - Nederlands Tijdschrift voor Natuurkunde - 31-05-2024
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Quantifying uncertainties in Direct Numerical Simulations of a turbulent channel flow
Get PDFDirect numerical simulation (DNS) provides unrivalled levels of detail and accuracy for simulating turbulent flows. However, like all numerical methods, DNS is subject to uncertainties arising from the numerical scheme and input parameters (e.g. mesh resolution). While uncertainty quantification (UQ) techniques are being employed more and more to provide a systematic analysis of uncertainty for lower-fidelity models, their application to DNS is still relatively rare. In light of this, the aim of this work is to apply UQ and sensitivity analysis to the DNS of a canonical wall-bounded turbulent channel flow at low Reynolds number (Reτ=180). To compute the DNS, Incompact3d – a highly scalable open-source framework based on high-order compact finite differences and a spectral Poisson solver – is used as a black-box solver. Stochastic collocation is used to propagate the input uncertainties through Incompact3d to the output quantities of interest (QOIs). To facilitate the non-intrusive forward UQ analysis, the open-source EasyVVUQ package is used to provide integrated capability for sampling, pre-processing, execution, post-processing, and analysis of the computational campaign. Three separate UQ campaigns are conducted. The first two examine the effect of domain size and the numerical parameters (e.g. mesh resolution, time step, sample time), respectively, and adopt Gaussian quadrature rules combined via tensor products to sample the multi-dimensional input space. Finally, the third campaign investigates the performance of a dimension-adaptive sampling strategy that significantly reduces the computational cost compared to the full tensor product approach. The analysis focuses on the cross-channel statistical moments of the QOIs, as well as local and global sensitivity analyses to assess the sensitivity of each QOI with respect to each individual input. This enables an assessment of the robustness and sensitivity of DNS to the user-defined numerical parameters for wall-bounded turbulent flows, and provides an indication of suitable ranges for defining the values of these parameters
Generic E-variables for exact sequential k-sample tests that allow for optional stopping
No full textWe develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact, nonasymptotic tests that remain safe, i.e., keep their type-I error guarantees, under flexible sampling scenarios such as optional stopping and continuation. In special cases our E-variables also have an optimal ‘growth’ property under the alternative. While the construction is generic, we illustrate it through the special case of k×2 contingency tables, i.e. k Bernoulli streams, allowing for the incorporation of different restrictions on the composite alternative. Comparison to p-value analysis in simulations and a real-world 2 × 2 contingency table example show that E-variables, through their flexibility, often allow for early stopping of data collection — thereby retaining similar power as classical methods — while also retaining the option of extending or combining data afterwards
Queerbench: Quantifying discrimination in language models toward queer identities
Get PDFWith the increasing role of Natural Language Processing (NLP) in various applications, challenges concerning bias and stereotype perpetuation are accentuated, which often leads to hate speech and harm. Despite existing studies on sexism and misogyny, issues like homophobia and transphobia remain underexplored and often adopt binary perspectives, putting the safety of LGBTQIA+ individuals at high risk in online spaces. In this paper, we assess the potential harm caused by sentence completions generated by English large language models (LLMs) concerning LGBTQIA+ individuals. This is achieved using QueerBench, our new assessment framework which employs a templatebased approach and a Masked Language Modeling (MLM) task. The analysis indicates that large language models tend to exhibit discriminatory behaviour more frequently towards individuals within the LGBTQIA+ community, reaching a difference gap of 7.2% in the QueerBench score of harmfulness
Energy-conserving hyper-reduction and temporal localization for reduced order models of the incompressible Navier-Stokes equations
Get PDFA novel hyper-reduction method is proposed that conserves kinetic energy and momentum for reduced order models of the incompressible Navier-Stokes equations. The main advantage of conservation of kinetic energy is that it endows the hyper-reduced order model (hROM) with a nonlinear stability property. The new method poses the discrete empirical interpolation method (DEIM) as a minimization problem and subsequently imposes constraints to conserve kinetic energy. Two methods are proposed to improve the robustness of the new method against error accumulation: oversampling and Mahalanobis regularization. Mahalanobis regularization has the benefit of not requiring additional measurement points. Furthermore, a novel method is proposed to perform energy- and momentum-conserving temporal localization with the principle interval decomposition: new interface conditions are derived such that energy and momentum are conserved for a full time-integration instead of only during separate intervals. The performance of the new energy- and momentum-conserving hyper-reduction methods and the energy- and momentum-conserving temporal localization method is analysed using three convection-dominated test cases; a shear-layer roll-up, two-dimensional homogeneous isotropic turbulence and a time-periodic inviscid flow consisting of a vortex in a uniform background flow. Our main finding is that energy conservation in combination with oversampling or regularization leads to a robust method with excellent long time stability properties. When any of these two ingredients is missing, accuracy and/or stability is significantly impaired
New foundations for separation logic
Get PDFThis thesis presents new foundations for separation logic, an important field within the formal sciences such as theoretical computer science. Around the turn of the millennium, separation logic was introduced by J.C. Reynolds with the goal to make reasoning, about the correctness of computer programs that work with so-called ‘pointers’, more efficient than earlier formal methods. Reynolds’ method and the other earlier methods are both extensions of the proof system introduced by C.A.R. Hoare for reasoning about the correctness of simple while-programs. The essence of Reynolds’ initial work, which was researched and put into practical use by many other scientists, consists of two extensions of the work initiated by Hoare: the first extension adds to first-order predicate logic two new propositional connectives (the so-called separating conjunction and separating implication); the second extension adds to Hoare’s program logic new proof rules for reasoning about (the primitive operations of) pointer programs. These primitive operations are used for reading memory (‘lookup’), writing memory (‘mutation’), reserving memory (‘allocation’), or freeing memory (‘deallocation’)
Hidden convexity, optimization, and algorithms on rotation matrices
Get PDFThis paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices SO(n). Such problems are nonconvex due to the constraint X∈SO(n). Nonetheless, we show that certain linear images of SO(n) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of SO(n) is convex and that the projection of SO(n) onto its strict upper triangular entries is convex. These results allow us to construct exact convex reformulations for constrained optimization problems over SO(n) with a single constraint or with constraints defined by low-rank matrices. Both of these results are optimal in a formal sense