Publications

Monographs

  • R. Henrion, Chapter 2: Calmness as a Constraint Qualification for M-Stationarity Conditions in MPECs, in: Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC, D. Aussel, C.S. Lalitha, eds., Forum for Interdisciplinary Mathematics, Springer, Singapore, 2018, pp. 21--41, (Chapter Published), DOI 10.1007/978-981-10-4774-9 .

Articles in Refereed Journals

  • W. VAN Ackooij, R. Henrion, P. Pérez-Aros, Generalized gradients for probabilistic/robust (probust) constraints, Optimization. A Journal of Mathematical Programming and Operations Research, published online on 14.02.2019, DOI 10.1080/02331934.2019.1576670 .
    Abstract
    Probability functions are a powerful modelling tool when seeking to account for uncertainty in optimization problems. In practice, such uncertainty may result from different sources for which unequal information is available. A convenient combination with ideas from robust optimization then leads to probust functions, i.e., probability functions acting on generalized semi-infinite inequality systems. In this paper we employ the powerful variational tools developed by Boris Mordukhovich to study generalized differentiation of such probust functions. We also provide explicit outer estimates of the generalized subdifferentials in terms of nominal data.

  • D. Hömberg, S. Lu, M. Yamamoto, Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data, Journal of Differential Equations, 266 (2019), pp. 7525--7544.
    Abstract
    We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.

  • R. Lasarzik, Measure-valued solutions to the Ericksen--Leslie model equipped with the Oseen--Frank energy, Nonlinear Analysis. An International Mathematical Journal, 179 (2019), pp. 146--183, DOI 10.1016/j.na.2018.08.013 .
    Abstract
    In this article, we prove the existence of measure-valued solutions to the Ericksen-Leslie system equipped with the Oseen--Frank energy. We introduce the concept of generalized gradient Young measures. Via a Galerkin approximation, we show the existence of weak solutions to a regularized system and attain measure-valued solutions for vanishing regularization. Additionally, it is shown that the measure-valued solution fulfills an energy inequality.

  • R. Lasarzik, Weak-strong uniqueness for measure-valued solutions to the Ericksen--Leslie model equipped with the Oseen--Frank free energy, Journal of Mathematical Analysis and Applications, 470 (2019), pp. 36--90, DOI 10.1016/j.jmaa.2018.09.051 .
    Abstract
    We analyze the Ericksen-Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of measure-valued solutions to this system and showed the global existence of these generalized solutions. In this paper, we show that suitable measure-valued solutions, which fulfill an associated energy inequality, enjoy the weak-strong uniqueness property, i.e. the measure-valued solution agrees with a strong solution if the latter exists. The weak-strong uniqueness is shown by a relative energy inequality for the associated nonconvex energy functional.

  • C. Brée, D. Gailevičius, V. Purlys, G.G. Werner, K. Staliunas, A. Rathsfeld, G. Schmidt, M. Radziunas, Chirped photonic crystal for spatially filtered optical feedback to a broad-area laser, Journal of Optics, 20 (2018), pp. 095804/1--095804/7, DOI 10.1088/2040-8986/aada98 .
    Abstract
    We derive and analyze an efficient model for reinjection of spatially filtered optical feedback from an external resonator to a broad area, edge emitting semiconductor laser diode. Spatial filtering is achieved by a chirped photonic crystal, with variable periodicity along the optical axis and negligible resonant backscattering. The optimal chirp is obtained from a genetic algorithm, which yields solutions that are robust against perturbations. Extensive numerical simulations of the composite system with our optoelectronic solver indicate that spatially filtered reinjection enhances lower-order transversal optical modes in the laser diode and, consequently, improves the spatial beam quality.

  • M. Eigel, J. Neumann, R. Schneider, S. Wolf, Risk averse stochastic structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 334 (2018), pp. 470--482, DOI 10.1016/j.cma.2018.02.003 .
    Abstract
    A novel approach for risk-averse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common risk-aware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such high-dimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach.

  • M. Eigel, M. Marschall, R. Schneider, Sampling-free Bayesian inversion with adaptive hierarchical tensor representations, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 34 (2018), pp. 035010/1--035010/29, DOI 10.1088/1361-6420/aaa998 .
    Abstract
    The statistical Bayesian approach is a natural setting to resolve the ill-posedness of inverse problems by assigning probability densities to the considered calibration parameters. Based on a parametric deterministic representation of the forward model, a sampling-free approach to Bayesian inversion with an explicit representation of the parameter densities is developed. The approximation of the involved randomness inevitably leads to several high dimensional expressions, which are often tackled with classical sampling methods such as MCMC. To speed up these methods, the use of a surrogate model is beneficial since it allows for faster evaluation with respect to calibration parameters. However, the inherently slow convergence can not be remedied by this. As an alternative, a complete functional treatment of the inverse problem is feasible as demonstrated in this work, with functional representations of the parametric forward solution as well as the probability densities of the calibration parameters, determined by Bayesian inversion. The proposed sampling-free approach is discussed in the context of hierarchical tensor representations, which are employed for the adaptive evaluation of a random PDE (the forward problem) in generalized chaos polynomials and the subsequent high-dimensional quadrature of the log-likelihood. This modern compression technique alleviates the curse of dimensionality by hierarchical subspace approximations of the involved low rank (solution) manifolds. All required computations can be carried out efficiently in the low-rank format. A priori convergence is examined, considering all approximations that occur in the method. Numerical experiments demonstrate the performance and verify the theoretical results.

  • L. Adam, M. Branda, H. Heitsch, R. Henrion, Solving joint chance constrained problems using regularization and Benders' decomposition, Annals of Operations Research, pp. published online on 08.11.2018, urlhttps://doi.org/10.1007/s10479-018-3091-9, DOI 10.1007/s10479-018-3091-9 .
    Abstract
    In this paper we investigate stochastic programms with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution.

  • E. Emmrich, S.H.L. Klapp, R. Lasarzik, Nonstationary models for liquid crystals: A fresh mathematical perspective, Journal of Non-Newtonian Fluid Mechanics, 259 (2018), pp. 32--47, DOI 10.1016/j.jnnfm.2018.05.003 .

  • E. Emmrich, R. Lasarzik, Existence of weak solutions to the Ericksen--Leslie model for a general class of free energies, Mathematical Methods in the Applied Sciences, 41 (2018), pp. 6492--6518.

  • E. Emmrich, R. Lasarzik, Weak-strong uniqueness for the general Ericksen--Leslie system in three dimensions, Discrete and Continuous Dynamical Systems, 38 (2018), pp. 4617--4635, DOI 10.3934/dcds.2018202 .

  • A. Hantoute, R. Henrion, P. Pérez-Aros, Subdifferential characterization of probability functions under Gaussian distribution, Mathematical Programming. A Publication of the Mathematical Programming Society, 174 (2019), pp. 167--194 (published online on 29.01.2018), DOI 10.1007/s10107-018-1237-9 .
    Abstract
    Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates the consideration of subdifferentials for such typically just continuous functions. The aim of this paper is to provide subdifferential formulae of such functions in the case of Gaussian distributions for possibly infinite-dimensional decision variables and nonsmooth (locally Lipschitzian) input data. These formulae are based on the spheric-radial decomposition of Gaussian random vectors on the one hand and on a cone of directions of moderate growth on the other. By successively adding additional hypotheses, conditions are satisfied under which the probability function is locally Lipschitzian or even differentiable.

  • M. Eigel, J. Neumann, R. Schneider, S. Wolf, Non-intrusive tensor reconstruction for high dimensional random PDEs, Computational Methods in Applied Mathematics, 19 (2019), pp. 39--53 (published online on 25.07.2018), DOI 10.1515/cmam-2018-0028 .
    Abstract
    This paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high dimensional parametric random PDEs which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to Monte Carlo sampling.

  • R. Henrion, W. Römisch, Problem-based optimal scenario generation and reduction in stochastic programming, Mathematical Programming. A Publication of the Mathematical Programming Society, pp. published online on 04.10.2018, urlhttps://doi.org/10.1007/s10107-018-1337-6, DOI 10.1007/s10107-018-1337-6 .
    Abstract
    Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear two-stage stochastic programs we show that the problem-based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi-infinite program. We show that the latter is convex if either right-hand sides or costs are random and can be transformed into a semi-infinite program in a number of cases. We also consider problem-based optimal scenario reduction for two-stage models and optimal scenario generation for chance constrained programs. Finally, we discuss problem-based scenario generation for the classical newsvendor problem.

  • R. Lasarzik, Dissipative solution to the Ericksen--Leslie system equipped with the Oseen--Frank energy, Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, pp. published online on 29.11.2018, urlhttps://doi.org/10.1007/s00033-018-1053-3, DOI 10.1007/s00033-018-1053-3 .
    Abstract
    We analyze the Ericksen-Leslie system equipped with the Oseen?Frank energy in three space dimensions. The new concept of dissipative solutions is introduced. Recently, the author introduced the concept of measure-valued solutions to the considered system and showed global existence as well as weak-strong uniqueness of these generalized solutions. In this paper, we show that the expectation of the measure valued solution is a dissipative solution. The concept of a dissipative solution itself relies on an inequality instead of an equality, but is described by functions instead of parametrized measures. These solutions exist globally and fulfill the weak-strong uniqueness property. Additionally, we generalize the relative energy inequality to solutions fulfilling different nonhomogeneous Dirichlet boundary conditions and incorporate the influence of a temporarily constant electromagnetic field. Relying on this generalized energy inequality, we investigate the long-time behavior and show that all solutions converge for the large time limit to a certain steady state.

Contributions to Collected Editions

  • M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Indexation strategies and calmness constants for uncertain linear inequality systems, in: The Mathematics of the Uncertain, E. Gil, E. Gil, J. Gil, M.Á. Gil, eds., 142 of Studies in Systems, Decision and Control, Springer, 2018, pp. 831--843.

Preprints, Reports, Technical Reports

  • F. Auricchio, E. Bonetti, M. Carraturo, D. Hömberg, A. Reali, E. Rocca, Structural multiscale topology optimization with stress constraint for additive manufacturing, Preprint no. 2615, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2615 .
    Abstract, PDF (2815 kByte)
    In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer.

  • R. Lasarzik, E. Rocca, G. Schimperna, Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model, Preprint no. 2608, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2608 .
    Abstract, PDF (338 kByte)
    In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], where the pointwise internal energy balance is replaced by the total energy inequality complemented with a weak form of the entropy inequality. Moreover, we prove existence of local-in-time strong solutions and, finally, we show weak-strong uniqueness of solutions, meaning that every weak solution coincides with a local strong solution emanating from the same initial data, as long as the latter exists.

  • J.I. Asperheim, P. Das, B. Grande, D. Hömberg, Th. Petzold, Numerical simulation of high-frequency induction welding in longitudinal welded tubes, Preprint no. 2600, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2600 .
    Abstract, PDF (3294 kByte)
    In the present paper the high-frequency induction (HFI) welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the joule heat term and nonlinear constitutive relations. Its main novelties are twofold: A new analytic approach permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process.

  • M. Eigel, L. Grasedyck, R. Gruhlke, D. Moser, Low rank surrogates for polymorphic fields with application to fuzzy-stochastic partial differential equations, Preprint no. 2580, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2580 .
    Abstract, PDF (1235 kByte)
    We consider a general form of fuzzy-stochastic PDEs depending on the interaction of probabilistic and non-probabilistic ("possibilistic") influences. Such a combined modelling of aleatoric and epistemic uncertainties for instance can be applied beneficially in an engineering context for real-world applications, where probabilistic modelling and expert knowledge has to be accounted for. We examine existence and well-definedness of polymorphic PDEs in appropriate function spaces. The fuzzy-stochastic dependence is described in a high-dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To aleviate this severe obstacle in practise, a compressed low-rank approximation of the problem formulation and the solution is derived. This is based on the Hierarchical Tucker format which is constructed with solution samples by a non-intrusive tensor reconstruction algorithm. The performance of the proposed model order reduction approach is demonstrated with two examples. One of these is the ubiquitous groundwater flow model with Karhunen-Loeve coefficient field which is generalized by a fuzzy correlation length.

  • M. Drieschner, M. Eigel, R. Gruhlke, D. Hömberg, Y. Petryna, Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations, Preprint no. 2579, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2579 .
    Abstract, PDF (6838 kByte)
    Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models.

  • J. Elschner, G. Hu, Inverse elastic scattering from rigid scatterers with a single incoming wave, Preprint no. 2571, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2571 .
    Abstract, PDF (383 kByte)
    The first part of this paper is concerned with uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the far-field pattern corresponding to a single elastic plane wave. Our approach is based on a new reflection principle for the first boundary value problem of the Navier equation. In the second part, we propose a revisited factorization method to recover a rigid elastic body with a single far-field pattern.

  • E. Emmrich, R. Lasarzik, Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations, Preprint no. 2567, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2567 .
    Abstract, PDF (381 kByte)
    A nonlinear model due to Soddemann et al. [37] and Stewart [38] describing incompressible smectic-A liquid crystals under flow is studied. In comparison to previously considered models, this particular model takes into account possible undulations of the layers away from equilibrium, which has been observed in experiments. The emerging decoupling of the director and the layer normal is incorporated by an additional evolution equation for the director. Global existence of weak solutions to this model is proved via a Galerkin approximation with eigenfunctions of the associated linear differential operators in the three-dimensional case.

  • M. Eigel, M. Marschall, M. Multerer, An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains, Preprint no. 2566, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2566 .
    Abstract, PDF (5791 kByte)
    A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework. The perturbation of the domain's boundary is described by a vector valued random field depending on a countable number of random variables in an affine way. The corresponding Karhunen-Loeve expansion is approximated by the pivoted Cholesky decomposition based on a prescribed covariance function. The examined high-dimensional Galerkin system follows from the domain mapping approach, transferring the randomness from the domain to the diffusion coefficient and the forcing. In order to make this computationally feasible, the representation makes use of the modern tensor train format for the implicit compression of the problem. Moreover, an a posteriori error estimator is presented, which allows for the problem-dependent iterative refinement of all discretization parameters and the assessment of the achieved error reduction. The proposed approach is demonstrated in numerical benchmark problems.

  • M. Eigel, R. Gruhlke, A hybrid FETI-DP method for non-smooth random partial differential equations, Preprint no. 2565, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2565 .
    Abstract, PDF (3236 kByte)
    A domain decomposition approach exploiting the localization of random parameters in high-dimensional random PDEs is presented. For high efficiency, surrogate models in multi-element representations are computed locally when possible. This makes use of a stochastic Galerkin FETI-DP formulation of the underlying problem with localized representations of involved input random fields. The local parameter space associated to a subdomain is explored by a subdivision into regions where the parametric surrogate accuracy can be trusted and where instead Monte Carlo sampling has to be employed. A heuristic adaptive algorithm carries out a problem-dependent hp refinement in a stochastic multi-element sense, enlarging the trusted surrogate region in local parametric space as far as possible. This results in an efficient global parameter to solution sampling scheme making use of local parametric smoothness exploration in the involved surrogate construction. Adequately structured problems for this scheme occur naturally when uncertainties are defined on sub-domains, e.g. in a multi-physics setting, or when the Karhunen-Loeve expansion of a random field can be localized. The efficiency of this hybrid technique is demonstrated with numerical benchmark problems illustrating the identification of trusted (possibly higher order) surrogate regions and non-trusted sampling regions.

  • W.M. Klesse, A. Rathsfeld, C. Gross, E. Malguth, O. Skibitzki, L. Zealouk, Fast scatterometric measurement of periodic surface structures in plasma-etching processes, Preprint no. 2564, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2564 .
    Abstract, PDF (4576 kByte)
    To satisfy the continuous demand of ever smaller feature sizes, plasma etching technologies in microelectronics processing enable the fabrication of device structures with dimensions in the nanometer range. In a typical plasma etching system a plasma phase of a selected etching gas is activated, thereby generating highly energetic and reactive gas species which ultimately etch the substrate surface. Such dry etching processes are highly complex and require careful adjustment of many process parameters to meet the high technology requirements on the structure geometry.
    In this context, real-time access of the structure's dimensions during the actual plasma process would be of great benefit by providing full dimension control and film integrity in real-time. In this paper, we evaluate the feasibility of reconstructing the etched dimensions with nanometer precision from reflectivity spectra of the etched surface, which are measured in real-time throughout the entire etch process. We develop and test a novel and fast reconstruction algorithm, using experimental reflection spectra taken about every second during the etch process of a periodic 2D model structure etched into a silicon substrate. Unfortunately, the numerical simulation of the reflectivity by Maxwell solvers is time consuming since it requires separate time-harmonic computations for each wavelength of the spectrum. To reduce the computing time, we propose that a library of spectra should be generated before the etching process. Each spectrum should correspond to a vector of geometry parameters s.t. the vector components scan the possible range of parameter values for the geometrical dimensions. We demonstrate that by replacing the numerically simulated spectra in the reconstruction algorithm by spectra interpolated from the library, it is possible to compute the geometry parameters in times less than a second. Finally, to also reduce memory size and computing time for the library, we reduce the scanning of the parameter values to a sparse grid.

  • M. Carraturo, E. Rocca, E. Bonetti, D. Hömberg, A. Reali, F. Auricchio, Additive manufacturing graded-material design based on phase-field and topology optimization, Preprint no. 2553, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2553 .
    Abstract, PDF (1965 kByte)
    In the present work we introduce a novel graded-material design for additive manufacturing based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology.

  • D. Adelhütte, D. Assmann, T. González Grandón, M. Gugat, H. Heitsch, R. Henrion, F. Liers, S. Nitsche, R. Schultz, M. Stingl, D. Wintergerst, Joint model of probabilistic-robust (probust) constraints with application to gas network optimization, Preprint no. 2550, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2550 .
    Abstract, PDF (8736 kByte)
    Optimization problems under uncertain conditions abound in many real-life applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually applied in case solutions are sought that are feasible for all realizations of uncertainties within some predefined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we introduce a class of joint probabilistic/robust constraints. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for finding their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound with high probability.

  • M. Eigel, P. Trunschke, R. Schneider, S. Wolf, Variational Monte Carlo -- Bridging concepts of machine learning and high dimensional partial differential equations, Preprint no. 2544, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2544 .
    Abstract, PDF (598 kByte)
    A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range of problems. A general unified convergence analysis is derived, which takes into account the approximation and the statistical errors. By this, a combination of theoretical results from numerical analysis and statistics is obtained. Numerical experiments illustrate the performance of the method with the model class of hierarchical tensors.

  • H. Heitsch, On probabilistic capacity maximization in a stationary gas network, Preprint no. 2540, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2540 .
    Abstract, PDF (379 kByte)
    The question for the capacity of a given gas network, i.e., determining the maximal amount of gas that can be transported by a given network, appears as an essential question that network operators and political administrations are regularly faced with. In that context we present a novel mathematical approach to assist gas network operators in managing uncertainty with respect to the demand and in exposing free network capacities while increasing reliability of transmission and supply. The approach is based on the rigorous examination of optimization problems with nonlinear probabilistic constraints. As consequence we deal with solving an optimization problem with joint probabilistic constraints over an infinite system of random inequalities. We will show that the inequality system can be reduced to a finite one in the situation of considering a tree network topology. A detailed study of the problem of maximizing free booked capacities in a stationary gas network is presented that comes up with an algebraic model involving Kirchhoff's first and second laws. The focus will be on both the theoretical and numerical side. We are going to validate a kind of rank two constraint qualification implying the differentiability of the considered capacity problem. At the numerical side we are going to solve the problem using a projected gradient decent method, where the function and gradient evaluations of the probabilistic constraints are performed by the approach of spheric-radial decomposition applied for multivariate Gaussian random variables and more general distributions.

  • R. Lasarzik, Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system, Preprint no. 2535, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2535 .
    Abstract, PDF (308 kByte)
    We analyze the Ericksen--Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the earlier introduced measure-valued solutions. In this article, we argue that dissipative solutions can be numerically approximated by a relative simple scheme, which fulfills the norm-restriction on the director in every step. We introduce a semi-discrete scheme and derive an approximated version of the relative-energy inequality for solutions of this scheme. Passing to the limit in the semi-discretization, we attain dissipative solutions. Additionally, we introduce an optimal control scheme, show the existence of an optimal control and a possible approximation strategy. We prove that the cost functional is lower semi-continuous with respect to the convergence of this approximation and argue that an optimal control is attained in the case that there exists a solution admitting additional regularity.

  • J. Yu, D. Hömberg, Th. Petzold, S. Lu, Temporal homogenization of a nonlinear parabolic system, Preprint no. 2524, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2524 .
    Abstract, PDF (982 kByte)
    In this paper we develop are two-scale model for a nonlinear parabolic system. Assuming a rapidly oscillating inhomogeneity with period ε for one equation we carry out a formal periodic expansion to obtain a homogenized equation coupled to a local in time cell problem. We justify the expansion by deriving an error estimate between the original and the two-scale model and show numerical simulations, which confirm the analytically derived error estimate.

  • G. Hu, A. Rathsfeld, Acoustic scattering from locally perturbed periodic surfaces, Preprint no. 2522, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2522 .
    Abstract, PDF (298 kByte)
    We prove well-posedness for the time-harmonic acoustic scattering of plane waves from locally perturbed periodic surfaces in two dimensions under homogeneous Dirichlet boundary conditions. This covers sound-soft acoustic as well as perfectly conducting, TE polarized electromagnetic boundary value problems. Our arguments are based on a variational method in a truncated bounded domain coupled with a boundary integral representation. If the quasi-periodic Green's function to the unperturbed periodic scattering problem is calculated efficiently, then the variational approach can be used for a numerical scheme based on coupling finite elements with a boundary element algorithm.
    Even for a general 2D rough-surface problem, it turns out that the Green's function defined with the radiation condition ASR satisfies the Sommerfeld radiation condition over the half plane. Based on this result, for a local perturbation of a periodic surface, the scattered wave of an incoming plane wave is the sum of the scattered wave for the unperturbed periodic surface plus an additional scattered wave satisfying Sommerfeld's condition on the half plane. Whereas the scattered wave for the unperturbed periodic surface has a far field consisting of a finite number of propagating plane waves, the additional field contributes to the far field by a far-field pattern defined in the half-plane directions similarly to the pattern known for bounded obstacles.

  • M. Eigel, M. Marschall, M. Pfeffer, R. Schneider, Adaptive stochastic Galerkin FEM for log-normal coefficients in hierarchical tensor representations, Preprint no. 2515, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2515 .
    Abstract, PDF (557 kByte)
    Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptive Galerkin FE method for linear parametric PDEs with log-normal coefficients discretized in Hermite chaos polynomials is derived. It employs problem-adapted function spaces to ensure solvability of the variational formulation. The inherently high computational complexity of the parametric operator is made tractable by using hierarchical tensor representations. For this, a new tensor train format of the lognormal coefficient is derived and verified numerically. The central novelty is the derivation of a reliable residual-based a posteriori error estimator. This can be regarded as a unique feature of stochastic Galerkin methods. It allows for an adaptive algorithm to steer the refinements of the physical mesh and the anisotropic Wiener chaos polynomial degrees. For the evaluation of the error estimator to become feasible, a numerically efficient tensor format discretization is developed. Benchmark examples with unbounded lognormal coefficient fields illustrate the performance of the proposed Galerkin discretization and the fully adaptive algorithm.

  • H. Heitsch, N. Strogies, Consequences of uncertain friction for the transport of natural gas through passive networks of pipelines, Preprint no. 2513, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2513 .
    Abstract, PDF (474 kByte)
    Assuming a pipe-wise constant structure of the friction coefficient in the modeling of natural gas transport through a passive network of pipes via semilinear systems of balance laws with associated linear coupling and boundary conditions, uncertainty in this parameter is quantified by a Markov chain Monte Carlo method. Here, information on the prior distribution is obtained from practitioners. The results are applied to the problem of validating technical feasibility under random exit demand in gas transport networks. In particular, the impact of quantified uncertainty to the probability level of technical feasible exit demand situations is studied by two example networks of small and medium size. The gas transport of the network is modeled by stationary solutions that are steady states of the time dependent semilinear problems.

  • R. Lasarzik, Dissipative solution to the Ericksen--Leslie system equipped with the Oseen--Frank energy, Preprint no. 2508, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2508 .
    Abstract, PDF (315 kByte)
    We analyze the Ericksen-Leslie system equipped with the Oseen?Frank energy in three space dimensions. The new concept of dissipative solutions is introduced. Recently, the author introduced the concept of measure-valued solutions to the considered system and showed global existence as well as weak-strong uniqueness of these generalized solutions. In this paper, we show that the expectation of the measure valued solution is a dissipative solution. The concept of a dissipative solution itself relies on an inequality instead of an equality, but is described by functions instead of parametrized measures. These solutions exist globally and fulfill the weak-strong uniqueness property. Additionally, we generalize the relative energy inequality to solutions fulfilling different nonhomogeneous Dirichlet boundary conditions and incorporate the influence of a temporarily constant electromagnetic field. Relying on this generalized energy inequality, we investigate the long-time behavior and show that all solutions converge for the large time limit to a certain steady state.

  • L. Adam, M. Branda, H. Heitsch, R. Henrion, Solving joint chance constrained problems using regularization and Benders' decomposition, Preprint no. 2471, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2471 .
    Abstract, PDF (236 kByte)
    In this paper we investigate stochastic programms with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution.

Talks, Poster

  • M.J. Arenas Jaén, Modeling, simulation and optimization of inductive pre- and post-heating for thermal cutting of steel plates, Workshop on Mathematics and Materials Science for Steel Production and Manufacturing, June 4 - 5, 2019, Thon Hotel Høyers, Skien, Norway, June 5, 2019.

  • C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broad-area diode lasers, CLEO/Europe-EQEC 2019, Munich, June 23 - 27, 2019.

  • R. Gruhlke, Bayesian upscaling with application to failure analysis of adhesiv bonds in rotor blades, 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Minisymposium 6--II ``Uncertainty Computations with Reduced Order Models and Low-Rank representations'', June 24 - 26, 2019, Crete, Greece, June 24, 2019.

  • R. Gruhlke, Polymorphic uncertainty propagation with application to failure analysis ofadhesive bonds in rotor blades, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Session ``DFG-PP 1886: Polymorphic uncertainty modelling for the numerical design of structures'', February 18 - 22, 2019, Technische Universität Wien, Austria, February 19, 2019.

  • H. Heitsch, On probabilistic capacity maximization in a stationary gas network, International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposia ``Mathematical Optimization and Gas Transport Networks: Academic Developments II'', July 15 - 19, 2019, Valencia, Spain, July 16, 2019.

  • M. Ebeling-Rump, Topology optimization subject to additive manufacturing constraints, INdAM Workshop MACH2019 ``Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage'', March 25 - 29, 2019, Istituto Nazionale di Alta Matematica "Francesco Severi", Rome, Italy, March 26, 2019.

  • M. Ebeling-Rump, Workshop on Numerical Methods for Optimal Control and Inverse Problems (OCIP 2019), March 11 - 13, 2019, Leibniz Supercomputing Centre (LRZ), Garching.

  • M. Eigel, A statistical learning approach for high-dimensional PDEs, 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Minisymposium 6--IV ``Uncertainty Computations with Reduced Order Models and Low-Rank representations'', June 24 - 26, 2019, Crete, Greece, June 25, 2019.

  • M. Eigel, A statistical learning approach for parametric PDEs, Workshop ``Scientific Computation using Machine-Learning Algorithms'', April 25 - 26, 2019, University of Nottingham, UK, April 26, 2019.

  • M. Eigel, A statistical learning approach for parametric PDEs, École polytechnique fédérale de Lausanne (EPFL), Scientific Computing and Uncertainty Quantification, Lausanne, Switzerland, May 14, 2019.

  • M. Eigel, Some thoughts on Adaptive Stochastic Galerkin FEM, Sixteenth Conference on the Mathematics of Finite Elements and Applications (MAFELAP 2019), Minisymposium 17 ``Finite Element Methods for Efficient Uncertainty Quantification'', June 18 - 21, 2019, Brunel University London, Uxbridge, UK, June 18, 2019.

  • R. Henrion, Chance constraints then and now, International Conference on Stochastic Optimization and Related Topics, April 25 - 26, 2019, Mühlheim an der Ruhr, April 26, 2019.

  • R. Henrion, On some extended models of chance constraints, Workshop ``Mathematical Optimization of Systems Impacted by Rare, High-Impact Random Events'', June 24 - 28, 2019, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, USA, June 24, 2019.

  • R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Spring School in Nonsmooth Analysis and Optimization, April 16 - 18, 2019, Université Mohammed V, Rabat, Morocco.

  • R. Henrion, Robust control of a sweeping process with probabilistic end-point constraints, Workshop ``Nonsmooth and Variational Analysis'', January 28 - February 1, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, January 31, 2019.

  • D. Hömberg, European collaboration in industrial and applied mathematics, EMMC International Workshop 2019 ``European Materials Modelling Council'', Wien, Austria, February 25 - 27, 2019.

  • D. Hömberg, From distortion compensation to 3D printing -- A phase field approach to topology optimization, The Hawassa Math & Stat Conference 2019, February 11 - 15, 2019, Hawassa University, Ethiopia, February 12, 2019.

  • D. Hömberg, MSO for steel production and manufacturing, International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposia ``Academia-Industry Case Studies from MI-NET and ECMI", July 15 - 19, 2019, Valencia, Spain, July 15, 2019.

  • R. Lasarzik, Optimal control via relative energies, Workshop ``Recent Trends in Optimal Control of Partial Differential Equations'', February 25 - 27, 2019, Technische Universität Berlin, February 27, 2019.

  • R. Lasarzik, Weak entropic solutions to a model in induction hardening: Existence and weak-strong uniqueness, Workshop ``Decima Giornata di Studio Università di Pavia -- Politecnico di Milano Equazioni Differenziali e Calcolo delle Variazioni'', Politecnico di Milano, Italy, February 21, 2019.

  • R. Lasarzik, Weak entropy solutions in the context of induction hardening, International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposia ``Partial Differential Equations VII'', July 15 - 19, 2019, Valencia, Spain, July 19, 2019.

  • M. Marschall, Adaptive low-rank approximation in Bayesian inverse problems, 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Minisymposium 6--IV ``Uncertainty Computations with Reduced Order Models and Low-Rank representations'', June 24 - 26, 2019, Crete, Greece, June 25, 2019.

  • M. Marschall, Random domains in PDE problems with low-rank surrogates. Forward and backward, Physikalisch-Technische Bundesanstalt, Berlin, April 10, 2019.

  • M.J. Arenas Jaén, Modelling, simulation and optimization of inductive pre-heating for thermal cutting of steel plates, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18 - 22, 2018, Budapest, Hungary, June 19, 2018.

  • L. Capone, Induction hardening of cam profiles: Modeling, simulation, and optimization, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18 - 22, 2018, Budapest, Hungary, June 19, 2018.

  • M. Eigel, Aspects of adaptive Galerkin FE for stochastic direct and inverse problems, Workshop ``Surrogate Models for UQ in Complex Systems'' (UNQW02), February 5 - 9, 2018, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, February 7, 2018.

  • R. Gruhlke, Domain decomposition and multi-scale failure analysis with polymorphic uncertainties for optimal design of rotor blades, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), March 19 - 23, 2018, Technische Universität München, March 22, 2018.

  • R. Gruhlke, Domain decomposition, random media and interaction, SPP 1886 Workshop ``Komplex C'', July 10 - 11, 2018, Ruhr-Universität Bochum, July 10, 2018.

  • R. Gruhlke, Stochastic domain decomposition and application in heterogeneous material, 3rd GAMM AGUQ Workshop on Uncertainty Quantification 2018, Technische Universität Dortmund, March 12 - 14, 2018.

  • H. Heitsch, A probabilistic approach to optimization in gas transport, 2nd Conference on Mathematics of Gas Transport (MoG-2), October 10 - 11, 2018, Konrad-Zuse-Zentrum für Informationstechnik Berlin, October 10, 2018.

  • H. Heitsch, Stochastic optimization with probabilistic/robust (probust) constraints, 23rd International Symposium on Mathematical Programming (ISMP 2018), Cluster: Optimization under Uncertainty, July 1 - 6, 2018, Bordeaux, France, July 2, 2018.

  • I. Bremer, Using an SQP-solver for nonlinear optimization under probabilistic constraints, 100th Meeting of the GOR Working Group ``Real World Mathematical Optimization'', April 12 - 13, 2018, Regenstauf, April 12, 2018.

  • M. Eigel, R. Gruhlke, Domain decomposition for random high-dimensional PDEs, Workshop ``Reducing Dimensions and Cost for UQ in Complex Systems'', Cambridge, UK, March 5 - 9, 2018.

  • M. Eigel, A statistical learning view on random PDEs, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), March 19 - 23, 2018, Technische Universität München, March 20, 2018.

  • M. Eigel, Adaptive Galerkin FEM for stochastic forward and inverse problems, Optimisation and Numerical Analysis Seminars, University of Birmingham, School of Mathematics, UK, February 15, 2018.

  • M. Eigel, Adaptive tensor methods for forward and inverse problems, SIAM Conference on Uncertainty Quantification (UQ18), Minisymposium 122 ``Low-Rank Approximations for the Forward- and the Inverse Problems III'', April 16 - 19, 2018, Garden Grove, USA, April 19, 2018.

  • R. Henrion, Dynamic chance constraints under continuous random distribution, PGMO DAYS 2018, Session 1E ``Stochastic Optimization'', November 20 - 21, 2018, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF'Lab Paris-Saclay, Palaiseau, France, November 21, 2018.

  • R. Henrion, Dynamic chance constraints under random distributions, 23rd International Symposium on Mathematical programming (ISMP 2018), Cluster: Optimization under Uncertainty, July 1 - 6, 2018, Bordeaux, France, July 5, 2018.

  • R. Henrion, Lipschitz properties and their moduli for constraint mappings, 4th Central European Set-Valued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, Philipps-Universität Marburg, November 24, 2018.

  • R. Henrion, M-stationary conditions for MPECs in finite dimension (Part 1+2), SPP 1962 Summer School on Complementarity Problems in Applied Mathematics: Modeling, Analysis, and Optimization, July 30 - August 1, 2018, Technische Universität Dortmund, July 31, 2018.

  • R. Henrion, Maximization of free capacities in gas networks with random load, Conference ``Variational Analysis -- Challenges in Energy'', June 4 - 6, 2018, Castro Urdiales, Spain, June 4, 2018.

  • R. Henrion, Optimization problems under probabilistic constraints, 3rd Russian-German Conference on MultiScale BioMathematics: Coherent Modeling of Human Body System, November 7 - 9, 2018, Lomonosov Moscow State University, Russian Federation, November 8, 2018.

  • R. Henrion, Optimization problems with probust constraints, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, June 28 - July 1, 2018, Martin-Luther-Universität Halle-Wittenberg, Halle, June 28, 2018.

  • R. Henrion, Perspectives in probabilistic programming under continuous random distributions, Workshop ``New Directions in Stochastic Optimisation'', August 19 - 25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 20, 2018.

  • R. Henrion, Probabilistic programming with applications, Universidad Miguel Hernández de Elche, Instituto Centro de Investigación Operativa, Spain, September 13, 2018.

  • R. Henrion, Verification and comparison of the calmness of generalized equations in original and enhanced form, International Workshop on Optimization and Variational Analysis, January 10 - 11, 2018, Termas de Cauquenes, Chile, January 11, 2018.

  • D. Hömberg, European collaboration in industrial and applied mathematics, Conference ``Mathematical Modelling in Metallurgical Industry'', September 17 - 18, 2018, Kristiansand, Norway, September 18, 2018.

  • D. Hömberg, European collaboration in industrial and applied mathematics, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, May 17, 2018.

  • D. Hömberg, European collaboration in industrial and applied mathematics, Inderprastha Engineering College, Ghaziabad, India, January 5, 2018.

  • D. Hömberg, Knowledge exchange in mathematics -- The European perspective, 1st IMA Conference on Knowledge Exchange in the Mathematical Sciences, December 3 - 4, 2018, Aston University, Birmingham, UK, December 3, 2018.

  • D. Hömberg, Mathematical challenges in steel manufacturing, Second International Conference on Modern Mathematical Methods and High Performance Computing in Science and Technology (M3HPCST 2018), January 4 - 6, 2018, Inderprastha Engineering College (IPEC), Ghaziabad, India, January 4, 2018.

  • D. Hömberg, Maths for digital factory, University of Southern Denmark, The Maersk Mc-Kinney Moller Institute, Odense, Denmark, October 12, 2018.

  • D. Hömberg, Temporal homogenization of a nonlinear parabolic system, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 15 ``Electromagnetic Problems Arising in Industry: Modelling and Numerical Techniques'', June 18 - 22, 2018, Budapest, Hungary, June 18, 2018.

  • R. Lasarzik, Generalised solutions to the Ericksen--Leslie model describing liquid crystal flow, Università degli Studi di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, June 7, 2018.

  • R. Lasarzik, Generalized solution concepts to the Ericksen--Leslie equations modeling liquid crystal flow, 28th IFIP TC 7 Conference on System Modelling and Optimization, July 23 - 27, 2018, Universität Duisburg-Essen, Essen, July 26, 2018.

  • M. Marschall, Bayesian inversion and adaptive low-rank tensor decomposition, 3rd GAMM AGUQ Workshop on Uncertainty Quantification 2018, Technische Universität Darmstadt, March 12 - 14, 2018.

  • M. Marschall, Bayesian inversion and adaptive low-rank tensor decomposition, Workshop ``UQ for Inverse Problems in Complex Systems'', Cambridge, UK, April 9 - 13, 2018.

  • M. Marschall, Bayesian inversion with adaptive low-rank approximation, Analysis, Control and Inverse Problems for PDEs -- Workshop of the French-German-Italian LIA (Laboratoire International Associe) COPDESC on Applied Analysis, November 26 - 30, 2018, University of Naples Federico II and Accademia Pontaniana, Italy, November 29, 2018.

  • M. Marschall, Bayesian inversion with adaptive low-rank approximation, Tensormeeting, November 26 - 27, 2018, Technische Universität Braunschweig, November 26, 2018.

  • M. Marschall, Surrogate model adaption by explicit Bayesian inversion in tensor train format, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), March 19 - 23, 2018, Technische Universität München, March 21, 2018.