SIAM UKIE National Student Chapter Conference

Selection acting on unmeasured individual variation is a common source of bias in the analysis of populations. It has been shown to affect measured rates of mortality, the survival of endangered species, the scope of neutral theories of biodiversity and molecular evolution, measured risks of diseases whether non-communicable or infectious, the efficacy of interventions such as vaccines or symbionts, and it may be an underappreciated cause for the reproducibility crisis that the life and social sciences currently travers.

Forms of variation that respond to selection and impact population dynamics, termed frailty variation in demography, remain elusive in many disciplines. I will present some examples, including how this appears to have affected the course of the coronavirus disease (COVID-19) pandemic.

In this talk, we will give an introduction to the field of multilevel optimization. To this end, we first focus on bilevel optimization problems and study their main properties. By doing so, we will see why this class of problems are very important for practice but we will also see why they are very challenging - both from a theoretical and from a practical point of view. Afterward, we discuss a recent application of multilevel optimization to model the European gas market as well as present and discuss some exemplary results for real-world data. Finally, we will illustrate how practical models need to be extended to cover uncertain aspects as well. This leads to a rather novel class of bilevel optimization problems for which we pose the open research question on whether they can be solved on a computer anyway.

Digital twin can be defined as a composable virtual representation of a system that can span its life cycle, is continuously updated from design and operational data, and can use simulation, machine learning, and reasoning to augment decision-making and / or control the system. Recent advances in computational workflows, physics-based solvers, big data processing and management tools bring the promise of digital twins and their impact on society closer to reality. One important enabling technology is surrogate modelling. The basic idea in the surrogate model approach is to invest resources in developing fast mathematical approximations to the long running computer codes or expensive physical experiments. Given these approximations, many questions can be posed and answered, many trade-offs explored, and insights gained. In this presentation, I will discuss different types of surrogate models and how they can be utilised advantageously in digital twin framework. I will focus on two areas: uncertainty quantification and system prediction for industrial applications.