Nichtlineare Optimierung und Inverse Probleme

Publikationen

Artikel in Referierten Journalen

• D. Hömberg, R. Lasarzik, L. Plato, On the existence of generalized solutions to a spatio-temporal predator-prey system, Journal of Evolution Equations, 23 (2023), pp. 20/1--20/44, DOI 10.1007/s00028-023-00871-5 .
  Abstract
  In this paper we consider a pair of coupled non-linear partial differential equations describing the interaction of a predator-prey pair. We introduce a concept of generalized solutions and show the existence of such solutions in all space dimension with the aid of a regularizing term, that is motivated by overcrowding phenomena. Additionally, we prove the weak-strong uniqueness of these generalized solutions and the existence of strong solutions at least locally-in-time for space dimension two and three.

• H. Heitsch, R. Henrion, Th. Kleinert, M. Schmidt, On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints, Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering, 84 (2022), pp. 651--685, DOI 10.1007/s10898-022-01161-z .
  Abstract
  Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.

• M. Branda, R. Henrion, M. Pištěk, Value at risk approach to producer's best response in electricity market with uncertain demand, Optimization. A Journal of Mathematical Programming and Operations Research, published online on 15.05.2022, DOI 10.1080/02331934.2022.2076232 .
  Abstract
  We deal with several sources of uncertainty in electricity markets. The independent system operator (ISO) maximizes the social welfare using chance constraints to hedge against discrepancies between the estimated and real electricity demand. We find an explicit solution of the ISO problem, and use it to tackle the problem of a producer. In our model, production as well as income of a producer are determined based on the estimated electricity demand predicted by the ISO, that is unknown to producers. Thus, each producer is hedging against the uncertainty of prediction of the demand using the value-at-risk approach. To illustrate our results, a numerical study of a producer's best response given a historical distribution of both estimated and real electricity demand is provided.

• K. El Karfi, R. Henrion, D. Mentagui, An agricultural investment problem subject to probabilistic constraints, Computational Management Science, 19 (2022), pp. 683--701, DOI 10.1007/s10287-022-00431-1 .

• G. Thiele, Th. Johanni, D. Sommer, J. Krüger, Decomposition of a cooling plant for energy efficiency optimization using OptTopo, Energies, 15 (2022), pp. 8387/1--8387/16, DOI 10.3390/en15228387 .

• X. Yu, G. Hu, W. Lu, A. Rathsfeld, PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface, SIAM Journal on Numerical Analysis, 60 (2022), pp. 2592--2625, DOI 10.1137/21M1439705 .
  Abstract
  This paper studies the perfectly-matched-layer (PML) method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation (BIE) solver. Along the vertical direction, we place a PML to truncate the unbounded domain onto a strip and prove that the PML solution converges to the true solution in the physical subregion of the strip with an error bounded by the reciprocal PML thickness. Laterally, we divide the unbounded strip into three regions: a region containing the defect and two semi-waveguide regions, separated by two vertical line segments. In both semi-waveguides, we prove the well-posedness of an associated scattering problem so as to well define a Neumann-to-Dirichlet (NtD) operator on the associated vertical segment. The two NtD operators, serving as exact lateral boundary conditions, reformulate the unbounded strip problem as a boundary value problem over the defected region. Due to the periodicity of the semi-waveguides, both NtD operators turn out to be closely related to a Neumann-marching operator, governed by a nonlinear Riccati equation. It is proved that the Neumann-marching operators are contracting, so that the PML solution decays exponentially fast along both lateral directions. The consequences culminate in two opposite aspects. Negatively, the PML solution cannot converge exponentially to the true solution in the whole physical region of the strip. Positively, from a numerical perspective, the Riccati equations can now be efficiently solved by a recursive doubling procedure and a high-accuracy PML-based BIE method so that the boundary value problem on the defected region can be solved efficiently and accurately. Numerical experiments demonstrate that the PML solution converges exponentially fast to the true solution in any compact subdomain of the strip.

• M. Ebeling-Rump, D. Hömberg, R. Lasarzik, Two-scale topology optimization with heterogeneous mesostructures based on a local volume constraint, Computers & Mathematics with Applications. An International Journal, 126 (2022), pp. 100--114, DOI 10.1016/j.camwa.2022.09.004 .
  Abstract
  A new approach to produce optimal porous mesostructures and at the same time optimizing the macro structure subject to a compliance cost functional is presented. It is based on a phase-field formulation of topology optimization and uses a local volume constraint (LVC). The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. The resulting optimal control problem is analysed mathematically, numerical results show its versatility in creating optimal macroscopic designs with tailored mesostructures.

• M. Eigel, R. Gruhlke, M. Marschall, Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion, Statistics and Computing, 32 (2022), pp. 27/1--27/27, DOI 10.1007/s11222-022-10087-1 .
  Abstract
  A novel method for the accurate functional approximation of possibly highly concentrated probability densities is developed. It is based on the combination of several modern techniques such as transport maps and nonintrusive reconstructions of low-rank tensor representations. The central idea is to carry out computations for statistical quantities of interest such as moments with a convenient reference measure which is approximated by an numerical transport, leading to a perturbed prior. Subsequently, a coordinate transformation leads to a beneficial setting for the further function approximation. An efficient layer based transport construction is realized by using the Variational Monte Carlo (VMC) method. The convergence analysis covers all terms introduced by the different (deterministic and statistical) approximations in the Hellinger distance and the Kullback-Leibler divergence. Important applications are presented and in particular the context of Bayesian inverse problems is illuminated which is a central motivation for the developed approach. Several numerical examples illustrate the efficacy with densities of different complexity.

• M. Eigel, R. Gruhlke, D. Moser, Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains, Computational Mechanics, 71 (2023), pp. 615--636 (published online on 27.12.2022), DOI 10.1007/s00466-022-02261-z .
  Abstract
  We develop a new fuzzy arithmetic framework for efficient possibilistic uncertainty quantification. The considered application is an edge detection task with the goal to identify interfaces of blurred images. In our case, these represent realisations of composite materials with possibly very many inclusions. The proposed algorithm can be seen as computational homogenisation and results in a parameter dependent representation of composite structures. For this, many samples for a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying effective material tensor map, an appropriate diffeomorphism is constructed to generate a family of meshes reflecting the possible material realisations. In the application, the uncertainty model is propagated through distance maps with respect to consecutive symmetry class tensors. Additionally, the efficacy of the best/worst estimate analysis of the homogenisation map as a bound to the average displacement for chessboard like matrix composites with arbitrary star-shaped inclusions is demonstrated.

• M. Eigel, O. Ernst, B. Sprungk, L. Tamellini, On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion, SIAM Journal on Numerical Analysis, 60 (2022), pp. 659--687, DOI 10.1137/20M1364722 .
  Abstract
  Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting.

• M. Eigel, M. Haase, J. Neumann, Topology optimisation under uncertainties with neural networks, Algorithms, 15 (2022), pp. 241/1--241/34, DOI https://doi.org/10.3390/a15070241 .

• M. Eigel, P. Trunschke, R. Schneider, Convergence bounds for empirical nonlinear least-squares, ESAIM: Mathematical Modelling and Numerical Analysis, 56 (2022), pp. 79--104, DOI 10.1051/m2an/2021070 .
  Abstract
  We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2 norm for which only a weighted Monte Carlo estimate can be computed. The objective is to obtain an approximation of an unknown target function by minimizing the empirical norm. In the case of linear subspaces it is well-known that such least squares approximations can become inaccurate and unstable when the number of samples is too close to the number of parameters. We review this statement for general nonlinear subsets and establish error bounds for the empirical best approximation error. Our results are based on a restricted isometry property (RIP) which holds in probability and we show sufficient conditions for the RIP to be satisfied with high probability. Several model classes are examined where analytical statements can be made about the RIP. Numerical experiments illustrate some of the obtained stability bounds.

• TH. Eiter, K. Hopf, R. Lasarzik, Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models, Advances in Nonlinear Analysis, 12 (2023), pp. 20220274/1--20220274/31 (published online on 03.10.2022), DOI 10.1515/anona-2022-0274 .
  Abstract
  We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject to two dissipation processes: one induced by a nonsmooth convex potential and one by stress diffusion. We show short-time existence of strong solutions as well as their uniqueness in a class of Leray--Hopf type weak solutions satisfying the tensorial component in the sense of an evolutionary variational inequality. The global-in-time existence of such generalized solutions has been established in a previous work. We further study the limit when stress diffusion vanishes. In this case, the above notion of generalized solutions is no longer suitable, and we introduce the concept of energy-variational solutions, which is based on an inequality for the relative energy. We derive general properties of energy-variational solutions and show their existence by passing to the non-diffusive limit in the relative energy inequality satisfied by generalized solutions for non-zero stress diffusion.

• R. Lasarzik, E. Rocca, G. Schimperna, Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model, Rendiconti Lincei -- Matematica e Applicazioni, 33 (2022), pp. 229--269, DOI 10.4171/RLM/970 .
  Abstract
  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.

Beiträge zu Sammelwerken

• G. Thiele, Th. Johanni, D. Sommer, M. Eigel, J. Krüger, OptTopo: Automated set-point optimization for coupled systems using topology information, in: 2022 8th International Conference on Control, Decision and Information Technologies (CoDIT), IEEE, 2022, pp. 224--229, DOI 10.1109/CoDIT55151.2022.9803985 .

Preprints, Reports, Technical Reports

• A. Rathsfeld, Simulating rough surfaces by periodic and biperiodic gratings, Preprint no. 2989, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2989 .
  Abstract, PDF (1180 kByte)
  The scattering of acoustic and electro-magnetic plane waves by rough surfaces is the subject of many books and papers. For simplicity, we consider the special case, described by a Dirichlet boundary value problem of the Helmholtz equation in the half space above the surface. We recall the formulae of the far-field pattern and the far-field intensity. The far-field can be defined formally for general rough surfaces. However, the derivation as asymptotic limits works only for waves, which decay for surface points tending to infinity. Comparing with the case of periodic surface structures, it is clear that the rigorous model of plane-wave scattering is accurate for the near field close to the surface. For the far field, however, the finite extent of the beams in the planes orthogonal to the propagation direction is to be taken into account. Doing this rigorously, leads to extremely expensive computations or is simply impossible. Therefore and to enable the approximation of waves above the rough surface by waves above periodic and biperiodic rough structures, we consider a simplified model of beams. The beam is restricted to a cylindrical domain around a ray in propagation direction, and the wave is equal to a plane wave inside of this domain and to zero outside. Based on this beam model, we derive the corresponding asymptotic formulae for the wave and its intensity. The intensity is equal to the formally defined far-field intensity multiplied by a simple cosine factor. Under special assumptions, the intensity for the rough surface can be approximated by that for rough periodic and biperiodic surface structures. In particular, we can cope with the case of shallow roughness, where the reflected intensity includes, besides the smooth density function w.r.t. the angular direction, a plane-wave beam propagating into the reflection direction of the planar mirror.
  Altogether, the main point of the paper is to fix the technical assumptions needed for the far-field formula of a simple beam model and for the approximation by the far fields of periodized rough surfaces. Furthermore, using the beam model, we discuss numerical experiments for rough surfaces defined as realizations of a random field and, to get a more practical case, the Dirichlet condition is replaced by a transmission condition. The far-field intensity function for a rough surface is the limit of intensity functions for periodized rough surfaces if the period tends to infinity. However, almost the same intensity function can be obtained with a fixed period by computing the average over many different realizations of the random field. Finally, we present numerical results for an inverse problem, where the parameters of the random field are sought from measured mean values of the intensities.

• M. Eigel, R. Gruhlke, D. Sommer, Less interaction with forward models in Langevin dynamics, Preprint no. 2987, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2987 .
  Abstract, PDF (1423 kByte)
  Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted covariance estimates rely on successive evaluations of the forward model or its gradient. A main drawback of these methods hence is their vast number of required forward calls as well as their possible lack of convergence in the case of more involved posterior measures such as multimodal distributions. The goal of this paper is to address these challenges to some extend. First, several possible adaptive ensemble enrichment strategies that successively enlarge the number of particles in the underlying Langevin dynamics are discusses that in turn lead to a significant reduction of the total number of forward calls. Second, analytical consistency guarantees of the ensemble enrichment method are provided for linear forward models. Third, to address more involved target distributions, the method is extended by applying adapted Langevin dynamics based on a homotopy formalism for which convergence is proved. Finally, numerical investigations of several benchmark problems illustrates the possible gain of the proposed method, comparing it to state-of-the-art Langevin samplers.

• M. Eigel, M. Haase, J. Neumann, Topology optimisation under uncertainties with neural networks, Preprint no. 2982, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2982 .
  Abstract, PDF (32 MByte)
  Topology optimisation is a mathematical approach relevant to different engineering problems where the distribution of material in a defined domain is distributed in some optimal way, subject to a predefined cost function representing desired (e.g., mechanical) properties and constraints. The computation of such an optimal distribution depends on the numerical solution of some physical model (in our case linear elasticity) and robustness is achieved by introducing uncertainties into the model data, namely the forces acting on the structure and variations of the material stiffness, rendering the task high-dimensional and computationally expensive. To alleviate this computational burden, we develop two neural network architectures (NN) that are capable of predicting the gradient step of the optimisation procedure. Since state-of-the-art methods use adaptive mesh refinement, the neural networks are designed to use a sufficiently fine reference mesh such that only one training phase of the neural network suffices. As a first architecture, a convolutional neural network is adapted to the task. To include sequential information of the optimisation process, a recurrent neural network is constructed as a second architecture. A common 2D bridge benchmark is used to illustrate the performance of the proposed architectures. It is observed that the NN prediction of the gradient step clearly outperforms the classical optimisation method, in particular since larger iteration steps become viable.

• M. Kirstein, M. Eigel, D. Sommer, Tensor-train kernel learning for Gaussian processes, Preprint no. 2981, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2981 .
  Abstract, PDF (355 kByte)
  We propose a new kernel learning approach based on efficient low-rank tensor compression for Gaussian process (GP) regression. The central idea is to compose a low-rank function represented in a hierarchical tensor format with a GP covariance function. Compared to similar deep neural network architectures, this approach facilitates to learn significantly more expressive features at lower computational costs as illustrated in the examples. Additionally, over-fitting is avoided with this compositional model by taking advantage of its inherent regularisation properties. Estimates of the generalisation error are compared to five baseline models on three synthetic and six real-world data sets. The experimental results show that the incorporated tensor network enables a highly accurate GP regression with a comparatively low number of trainable parameters. The observed performance is clearly superior (usually by an order of magnitude in mean squared error) to all examined standard models, in particular to deep neural networks with more than 1000 times as many parameters.

• TH. Eiter, R. Lasarzik, Existence of energy-variational solutions to hyperbolic conservation laws, Preprint no. 2974, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2974 .
  Abstract, PDF (546 kByte)
  oduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions is convex and weakly-star closed. The existence of energy-variational solutions is proven via a suitable time-discretization scheme under certain assumptions. This general result yields existence of energy-variational solutions to the magnetohydrodynamical equations for ideal incompressible fluids and to the Euler equations in both the incompressible and the compressible case. Moreover, we show that energy-variational solutions to the Euler equations coincide with dissipative weak solutions.

• R. Lasarzik, M.E.V. Reiter, Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations, Preprint no. 2966, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2966 .
  Abstract, PDF (8159 kByte)
  We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.

• M. Gugat, H. Heitsch, R. Henrion, A turnpike property for optimal control problems with dynamic probabilistic constraints, Preprint no. 2941, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2941 .
  Abstract, PDF (354 kByte)
  In this paper we consider systems that are governed by linear time-discrete dynamics with an initial condition, additive random perturbations in each step and a terminal condition for the expected values. We study optimal control problems where the objective function consists of a term of tracking type for the expected values and a control cost. In addition, the feasible states have to satisfy a conservative probabilistic constraint that requires that the probability that the trajectories remain in a given set F is greater than or equal to a given lower bound. An application are optimal control problems related to storage management systems with uncertain in- and output. We give sufficient conditions that imply that the optimal expected trajectories remain close to a certain state that can be characterized as the solution of an optimal control problem without prescribed initial- and terminal condition. In this way we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics and make a step towards the extension of the turnpike theory to problems with probabilistic constraints.

• M. Drieschner, R. Gruhlke, Y. Petryna, M. Eigel, D. Hömberg, Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains, Preprint no. 2928, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2928 .
  Abstract, PDF (9378 kByte)
  Imperfections and inaccuracies in real technical products often influence the mechanical behavior and the overall structural reliability. The prediction of real stress states and possibly resulting failure mechanisms is essential and a real challenge, e.g. in the design process. In this contribution, imperfections in elastic materials such as air voids in adhesive bonds between fiber-reinforced composites are investigated. They are modeled as arbitrarily shaped and positioned. The focus is on local displacement values as well as on associated stress concentrations caused by the imperfections. For this purpose, the resulting complex random one-scale finite element model is numerically solved by a new developed surrogate model using an overlapping domain decomposition scheme based on Schwarz alternating method. Here, the actual response of local subproblems associated with isolated material imperfections is determined by a single appropriate surrogate model, that allows for an accelerated propagation of randomness. The efficiency of the method is demonstrated for imperfections with elliptical and ellipsoidal shape in 2D and 3D and extended to arbitrarily shaped voids. For the latter one, a local surrogate model based on artificial neural networks (ANN) is constructed. Finally, a comparison to experimental results validates the numerical predictions for a real engineering problem.

• R. Gruhlke, M. Eigel, Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport, Preprint no. 2927, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2927 .
  Abstract, PDF (10 MByte)
  A unsupervised learning approach for the computation of an explicit functional representation of a random vector Y is presented, which only relies on a finite set of samples with unknown distribution. Motivated by recent advances with computational optimal transport for estimating Wasserstein distances, we develop a new Wasserstein multi-element polynomial chaos expansion (WPCE). It relies on the minimization of a regularized empirical Wasserstein metric known as debiased Sinkhorn divergence.

  As a requirement for an efficient polynomial basis expansion, a suitable (minimal) stochastic coordinate system X has to be determined with the aim to identify ideally independent random variables. This approach generalizes representations through diffeomorphic transport maps to the case of non-continuous and non-injective model classes M with different input and output dimension, yielding the relation Y=M(X) in distribution. Moreover, since the used PCE grows exponentially in the number of random coordinates of X, we introduce an appropriate low-rank format given as stacks of tensor trains, which alleviates the curse of dimensionality, leading to only linear dependence on the input dimension. By the choice of the model class M and the smooth loss function, higher order optimization schemes become possible. It is shown that the relaxation to a discontinuous model class is necessary to explain multimodal distributions. Moreover, the proposed framework is applied to a numerical upscaling task, considering a computationally challenging microscopic random non-periodic composite material. This leads to tractable effective macroscopic random field in adopted stochastic coordinates.

Vorträge, Poster

• M. Eigel, Convergence of an empirical Galerkin method for parametric PDEs, SIAM Conference on Computational Science and Engineering (CSE23), MS100: "Randomized Solvers in Large-Scale Scientific Computing (Part I)", February 26 - March 3, 2023, Amsterdam, Netherlands, February 28, 2023.

• L. Plato, Biological pest control -- Analysis and numerics for a spatio-temporal predator-prey system (online talk), Technische Universität Berlin, Institut für Mathematik, January 10, 2022.

• L. Plato, Generalized solutions in the context of a nonlocal predetor-prey model (online talk), SIAM Conference on Analysis of Partial Differential Equations (PD22), Minisymposium ``Generalized Solvability Concepts for Evolutionary PDEs and their Properties" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 16, 2022.

• J. Schütte, Adaptive neural networks for parametric PDE, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), PP04: ``Theoretical Foundations of Deep Learning'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

• J. Schütte, Adaptive neural networks for parametric PDEs, Annual Meeting of SPP 2298, November 20 - 23, 2022, Evangelische Akademie, Tutzing, November 21, 2022.

• J. Schütte, Adaptive neural tensor networks for parametric PDEs, Workshop on the Approximation of Solutions of High-Dimensional PDEs with Deep Neural Networks within the DFG Priority Programme 2298 ``Theoretical Foundations of Deep Learning'', May 30 - 31, 2022, Universität Bayreuth, May 31, 2022.

• M. Eigel, Empirical adaptive Galerkin FEM for parametric PDEs, 10th International Conference on Curves and Surfaces, Minisymposium 13 ``High dimensional approximation and PDEs'', June 20 - 24, 2022, Arcachon, France, June 23, 2022.

• R. Gruhlke, Annual report 2022 -- MuScaBlaDes (subproject 4 within SPP1886), Jahrestreffen des SPP 1886, Rheinisch-Westfälische Technische Hochschule Aachen, August 17, 2022.

• R. Gruhlke, Wasserstein polynomial chaos expansion with application to computational homogenization and Baysian inference, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Session 15: ``Uncertainty Quantification'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

• H. Heitsch, An algorithmic approach for solving optimization problems with probabilistic/robust (probust) constraints (online talk), TRR154 Summer School on Modelling, Simulation and Optimization for Energy Networks (Online Event), June 8 - 9, 2022, June 8, 2022.

• D. Sommer, Dynamical low rank approximation in molecular dynamics and optimal control, MASCOT-NUM 2022, June 7 - 9, 2022, Clermont Ferrand, France, June 7, 2022.

• D. Sommer, Less interaction with forward models in Langerin dynamics, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Session 15: ``Uncertainty Quantification'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

• D. Sommer, Tensor-train kernel learning for Gaussian processes (online talk), 11th Symposium on Conformal and Probabilistic Prediction with Applications (COPA 2022) (Hybrid Event), Paper session: ``Machine Learning 1'', August 24 - 26, 2022, University of Brighton, UK, August 25, 2022.

• M. Eigel, Adaptive Galerkin FEM for non-affine linear parametric PDEs, Computational Methods in Applied Mathematics (CMAM 2022), MS06: ``Computational Stochastic PDEs'', August 29 - September 2, 2022, Technische Universität Wien, Austria, August 29, 2022.

• M. Eigel, An empirical adaptive Galerkin method for parametric PDEs, Workshop ``Adaptivity, High Dimensionality and Randomness'' (Hybrid Event), April 4 - 8, 2022, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, April 6, 2022.

• R. Henrion, A turnpike property for a discrete-time linear optimal control problem with probabilistic constraints, Workshop on Optimal Control Theory, June 22 - 24, 2022, Institut National des Sciences Appliquées Rouen Normandie, Rouen, France, June 24, 2022.

• R. Henrion, A turnpike property for an optimal control problem with chance constraints, PGMO DAYS 2022, Session 15F: ``New Developments in Optimal Control Theory, Part II'', November 28 - 30, 2022, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF Lab Paris-Saclay, Palaiseau, France, November 29, 2022.

• R. Henrion, Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions (online talk), Seminar on Variational Analysis and Optimization, University of Michigan, Department of Mathematics, Ann Arbor, USA, February 17, 2022.

• R. Henrion, Probabilistic constraints via spherical-radial decomposition. Part I (online talk), Seminar on Variational Analysis and Optimization, Western Michigan University, Kalamazoo, USA, February 4, 2022.

• R. Henrion, Probabilistic constraints via spherical-radial decomposition. Part II (online talk), Western Michigan University, Kalamazoo, USA, February 11, 2022.

• D. Hömberg, A phasefield approach to two-scale topology optimization, DNA Seminar (Hybrid Event), Norwegian University of Science and Technology, Department of Mathematical Sciences, Norway, March 14, 2022.

• D. Hömberg, On two-scale topology optimization (online talk), Workshop ``Practical Inverse Problems and Their Prospects'' (Online Event), March 2 - 4, 2022, Kyushu University, Japan, March 4, 2022.

• M. Landstorfer, A. Selahi, M. Heida, M. Eigel, Recovery of battery ageing dynamics with multiple timescales, MATH+-Day 2022, Technische Universität Berlin, November 18, 2022.

• R. Lasarzik, Energy-variational solutions for conservation laws, DMV Annual Meeting 2022, September 12 - 16, 2022, Freie Universität Berlin, September 14, 2022.

• R. Lasarzik, Energy-variational solutions in the context of incompressible fluid dynamics (online talk), SIAM Conference on Analysis of Partial Differential Equations (PD22), MS 47: ``Generalized Solvability Concepts for Evolutionary PDEs and their Properties'' (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 16, 2022.