## NDNS+

#### Optimal-Experimental-Design Strategies for Hyper-Parametrized Inverse Problems

In this talk, we consider the problem of optimal experimental design in the context of inverse problems involving systems governed by parametrised (partial) differential equations.  In such inverse problems, the goal is often to infer from measurement data the values of unknown or uncertain parameters and thereby more accurately predict the state.  However, when measurements are costly, it is important to choose the most informative data.  This task becomes even more challenging when the model contains additional uncertainties and when the data noise is correlated.  In this context, I will discuss optimal experimental design strategies for hyper-parametrized families of PDE-constrained inverse problems.  With the help of reduced order models, the proposed method iteratively chooses the experiments that increase the stability of the inverse problem and decrease the uncertainty in the solution, and is suitable even for large-scale problems with correlated noise.

#### Mimetic methods within scientific computing

Basic education in scientific computing, also known as numerical analysis, often consists of standard methods that are based upon general principles such as Taylor series expansions. Examples are the large collection of discretisation methods, interpolation techniques such as Lagrange and Hermite, and methods for solving nonlinear systems such as Newton’s method. Such methods do not use any information about the underlying problem. Challenges in industry often require robust, fast and efficient scientific computing methods. This can be achieved by using knowledge about the problem and its solution. It is important to teach our students how they can develop and use such methods, and be fully prepared for numerical work in an industrial environment. Such methods are termed mimetic methods, i.e. methods that mimic the behaviour of the underlying problem. When searching the internet, one will observe that most of such methods have been formulated in the area of discretisation. Examples are exponentially fitted discretisation schemes, or numerical methods guaranteeing physical conservation laws and maximum principles. However, the field of mimetic methods is much broader. The well-known method ICCG for iteratively solving large linear systems is a mimetic method. In the area of model order reduction, we have developed index preserving MOR for differential-algebraic systems. Nonlinear systems can be solved using the method of correction transformation, which has been extremely effective for the simulation of semiconductor devices. In the area of port-Hamiltonian systems, special mimetic methods have been developed.

In this presentation, we will provide a summary of mimetic methods and identify many areas within scientific computing where such methods have been developed and successfully applied to industrial challenges. In my opinion, mimetic methods are the way forward in scientific computing.

#### Renewal equations and epidemic models

The first aim of the talk is to highlight the renewal equation formulation of epidemic models as introduced by Kermack and McKendrick in 1927.The second aim is to survey some recently developed tools (pseudo-spectral approximation, time discretization) for analysing this class of delay equations.(Here a delay equation is defined as a rule for extending a function of time towards the future on the basis of the (assumed to be) known past.)