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Mean robust optimization
No full textRobust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing a trade-off between computational effort and conservatism. We propose uncertainty sets constructed based on clustered data rather than on observed data points directly thereby significantly reducing problem size. By varying the number of clusters, our method bridges between robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential additional pessimism introduced by any clustering procedure. In addition, we prove conditions for which, when the uncertainty enters linearly in the constraints, clustering does not affect the optimal solution. We illustrate the efficiency and performance preservation of our method on several numerical examples, obtaining multiple orders of magnitude speedups in solution time with little-to-no effect on the solution quality
Energy-consistent discretization of viscous dissipation with application to natural convection flow
Get PDFA new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the ‘implied’ presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation. Numerical experiments of Rayleigh–Bénard convection (RBC) and Rayleigh–Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids. Therefore, the proposed discretization also forms an excellent starting point for testing sub-grid scale models and is a useful tool to assess energy budgets in any turbulence simulation, with or without the presence of natural convection
Live game design: Prototyping at the speed of play
Get PDFAutomated Game Design empowers game designers with languages,
techniques and tools that automate iterative design processes. How-
ever, these tools currently lack suitable input and feedback mecha-
nisms for creating rules and perceiving how changes affect running
game prototypes. As a result, iterating takes too long, forming
mental models about cause-and-effect relationships is difficult, and
learning how to program can be tedious and frustrating. We investi-
gate how Live Programming can accelerate game design iterations,
make visual tools more accessible and engaging, and provide im-
mediate feedback that brings code to life. We propose Live Game
Design, a novel approach for rapid game prototyping that intro-
duces mini-cycles to help designers of all skill levels explore, learn,
and see a prototype come alive. We introduce Vie (pronounced /vi/),
a game-making game for simultaneously prototyping and playtest-
ing simple 2D games using Machinations. In an observational study,
we evaluate the app during a Game-Based Learning tutorial for
children aged 8 to 14. Our results show Vie is accessible to novices
and Live Game Design enables prototyping at the speed of play
Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees
Get PDFWe show that the anti-ferromagnetic Potts model on trees exhibits strong spatial mixing for a near-optimal range of parameters. Our work complements recent results of Chen, Liu, Mani, and Moitra [CLMM23] who showed this to be true in the infinite temperature setting, corresponding to uniform proper colorings. We furthermore prove weak spatial mixing results complementing results in [CLMM23]
Ik zie, ik zie wat jij niet ziet... de wiskunde achter röntgentomografie
Get PDFWat zit er verstopt in een mummie? Hoe oud is een houten beeldje? Wat staat er geschreven op een papyrusrol? Deze vragen kunnen we natuurlijk beantwoorden door de mummie uit te wikkelen of het beeldje door te zagen. Maar liever doen we het op een subtielere manier, zonder het object te beschadigen. Dat kan door het te scannen in een Röntgenscanner en het daarna digitaal uit te rollen of door te zagen. We kennen CT-scanners natuurlijk ook uit het ziekenhuis, waar er mensen mee worden gescand om bijvoorbeeld botbreuken en hersenletsels te bekijken. In een CT-scanner worden Röntgenfoto's gemaakt, en daarna worden deze 2D foto's gecombineerd tot een 3D plaatje met behulp van een reconstructie-algoritme. In deze voordracht gaan we dieper in op hoe dat in zijn werk gaat, en leggen we de link met Japanse puzzels en stelsels vergelijkingen. We zien dat een klein beetje wiskunde al heel nuttig is in allerlei praktische toepassingen, van het ziekenhuis tot het museum
E-values for anytime-valid inference with exponential families
Get PDFStatistical hypothesis testing is vital across academic disciplines and industries. For example, in medicine, it plays a crucial role in drug development by guiding decisions on a drug’s efficacy and safety. Traditional hypothesis testing requires researchers to set a fixed sample size in advance. After collecting data, the test determines whether to reject the null hypothesis. In contrast, modern approaches like anytime-valid tests (e.g., methods based on e-values and e-processes) provide greater flexibility. These methods allow researchers to assess evidence continuously as data is gathered, eliminating the need for a pre-determined sample size. E-values, in particular, do not require predefined stopping rules for the experiment. This dissertation focuses on the analysis and application of e-values and e-processes within exponential families
Disentangling spring-neap suspended particulate matter (SPM) dynamics in estuaries
Get PDFSuspended particulate matter (SPM) concentrations in estuaries have been observed to vary strongly over the spring-neap cycle through complex interactions between trapping and re-suspension. However, a systematic framework for analysing the processes causing this spring-neap SPM variability in general is missing. In this study we set up such a framework, consisting of three tiers. First, by studying the sediment transport capacity, how the locations of sediment trapping change over the spring-neap cycle is identified. Second, how the transport capacity affects the sediment stock and bottom pool of sediment is studied. This bottom pool only adapts gradually to the changing transport conditions, incorporating a lag or memory effect. Using a two-timescale analysis it is shown that this slow movement of the bottom pool is the leading source of such lag effects. Third, the SPM concentration is explained from an almost instantaneously balanced exchange between the bottom pool and the water column through re-suspension and deposition. We demonstrate the use of this framework on two model cases implemented in the idealised width-averaged iFlow model: an idealised test case where the sediment dynamics do not affect the water motion and a case representative of the Loire estuary, with strong feedback between sediment and the water motion through sediment-induced damping of turbulence. The first is illustrative as it allows a full understanding in terms of cause and effect between water motion, transport, and SPM concentration. In the more realistic Loire case, the SPM dynamics cannot be explained in terms of cause and effect but can explain the trapping locations and timing of maximum concentrations in a systematic way in terms of the governing physical mechanisms
Polyhedral restrictions of feasibility regions in optimal power flow for distribution networks
No full textThe optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints) lay the foundation for the feasibility region of the OPF problem. While significant research has focused on convex relaxations, which are approaches to solve an OPF problem by enlarging the true feasibility region, the opposite approach of convex restrictions offers valuable insights as well. Convex restrictions, including polyhedral restrictions, reduce the true feasible region to a convex region, ensuring that it contains only feasible points. In this work, we develop a sequential optimization method that offers a scalable way to obtain (bounds on) solutions to OPF problems for distribution networks. To do so, we first develop sufficient conditions for the existence of feasible power flow solutions in the neighborhood of a specific (feasible) operating point in distribution networks, and second, based on these conditions, we construct a polyhedral restriction of the feasibility region. Our numerical results demonstrate the efficacy of the sequential optimization method as an alternative to existing approaches to obtain (bounds on) solutions to OPF problems for distribution networks. By construction, the optimization problems within the defined restrictions can be solved in polynomial time and are guaranteed to have feasible solutions