Nonlinear Optimization and Inverse Problems

Publications

Articles in Refereed Journals

• H. Heitsch, R. Henrion, C. Tischendorf, Probabilistic maximization of time-dependent capacities in a gas network, Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences, published online on 06.08.2024, DOI 10.1007/s11081-024-09908-1 .
  Abstract
  The determination of free technical capacities belongs to the core tasks of a gas network owner. Since gas loads are uncertain by nature, it makes sense to understand this as a probabilistic problem as far as stochastic modeling of available historical data is possible. Future clients, however, don't have a history or they do not behave in a random way, as is the case, for instance, in gas reservoir management. Therefore, capacity maximization turns into an optimization problem with uncertainty-related constrained which are partially of probabilistic and partially of robust (worst case) type. While previous attempts to solve this problem had be devoted to models with static (time-independent) gas flow, we aim at considering here transient gas flow subordinate to a PDE (Euler equations). The basic challenge here is two-fold: first, a proper way of joining probabilistic constraints to the differential equations has to be found. This will be realized on the basis of the so-called spherical-radial decomposition of Gaussian random vectors. Second, a suitable characterization of the worst-case load behaviour of future customers has to be figured out. It will be shown, that this is possible for quasi-static flow and can be transferred to the transient case. The complexity of the problem forces us to constrain ourselves in this first analysis to simple pipes or to a V-like structure of the network. Numerical solutions are presented and show that the differences between quasi-static and transient solutions are small, at least in these elementary examples.

• N. Ouanes, T. González Grandón, H. Heitsch, R. Henrion, Optimizing the economic dispatch of weakly-connected mini-grids under uncertainty using joint chance constraints, Annals of Operations Research, 344 (2025), pp. 499--531 (published online on 25.09.2024), DOI 10.1007/s10479-024-06287-9 .
  Abstract
  In this paper, we deal with a renewable-powered mini-grid, connected to an unreliable main grid, in a Joint Chance Constrained (JCC) programming setting. In several rural areas in Africa with low energy access rates, grid-connected mini-grid system operators contend with four different types of uncertainties: forecasting errors of solar power and load; frequency and outages duration from the main-grid. These uncertainties pose new challenges to the classical power system's operation tasks. Three alternatives to the JCC problem are presented. In particular, we present an Individual Chance Constraint (ICC), Expected-Value Model (EVM) and a so called regular model that ignores outages and forecasting uncertainties. The JCC model has the capability to guarantee a high probability of meeting the local demand throughout an outage event by keeping appropriate reserves for Diesel generation and battery discharge. In contrast, the easier to handle ICC model guarantees such probability only individually for different time steps, resulting in a much less robust dispatch. The even simpler EVM focuses solely on average values of random variables. We illustrate the four models through a comparison of outcomes attained from a real mini-grid in Lake Victoria, Tanzania. The results show the dispatch modifications for battery and Diesel reserve planning, with the JCC model providing the most robust results, albeit with a small increase in costs.

• A. Agosti, R. Lasarzik, E. Rocca, Energy-variational solutions for viscoelastic fluid models, Advances in Nonlinear Analysis, 13, pp. 20240056/1--20240056/35, DOI 10.1515/anona-2024-0056 .
  Abstract
  In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be shown constructively by an adapted minimizing movement scheme. Weak-strong uniqueness follows by a suitable relative energy inequality.
  Our main motivation is to apply the general framework to viscoelastic fluid models. Therefore, we give a short overview on different versions of such models and their derivation. The abstract result is applied to two of these viscoelastic fluid models in full detail. In the conclusion, we comment on further applications of the general theory and its possible impact.

• J.I. Asperheim, P. Das, B. Grande, D. Hömberg, Th. Petzold, Numerical simulation of high-frequency induction welding in longitudinal welded tubes, Journal of Mathematics in Industry, 14 (2024), pp. 10/1- -10/21, DOI 10.1186/s13362-024-00147-8 .
  Abstract
  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.

• H. Brüggemann, A. Paulsen, K. Oppedal, M. Grasmair, D. Hömberg, Reliably calibrating X-ray images required for preoperative planning of THA using a device-adapted magnification factor, PLOS ONE, 19 (2024), pp. e0307259/1--e0307259/11, DOI 10.1371/journal.pone.0307259 .

• G. Hu, A. Rathsfeld, Radiation conditions for the Helmholtz equation in a half plane filled by inhomogeneous periodic material, Journal of Differential Equations, 388 (2024), pp. 215--252, DOI 10.1016/j.jde.2024.01.008 .
  Abstract
  In this paper we consider time-harmonic acoustic wave propagation in a half-plane filled by inhomogeneous periodic medium. If the refractive index depends on the horizontal coordinate only, we define upward and downward radiating modes by solving a one-dimensional Sturm-Liouville eigenvalue problem with a complex-valued periodic coefficient. The upward and downward radiation conditions are introduced based on a generalized Rayleigh series. Using the variational method, we then prove uniqueness and existence for the scattering of an incoming wave mode by a grating located between an upper and lower half plane with such inhomogeneous periodic media. Finally, we discuss the application of the new radiation conditions to the scattering matrix algorithm, i.e., to rigorous coupled wave analysis or Fourier modal method.

• W. VAN Ackooij, R. Henrion, H. Zidani, Pontryagin's principle for some probabilistic control problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 90 (2024), pp. 5/1--5/36, DOI 10.1007/s00245-024-10151-4 .
  Abstract
  In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the objective function or constraints to define optimal or feasible controls. We provide an extension of differentiability results for probability functions in infinite dimensions usable in this context. These results are subsequently combined with the optimal control setting to derive a novel Pontryagin's optimality principle.

• C. Geiersbach, R. Henrion, Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form, Mathematics of Operations Research, published online on 15.07.2024, DOI 10.1287/moor.2023.0177 .
  Abstract
  In this paper, we discuss optimality conditions for optimization problems subject to random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation (PDE) with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them to a model based on robust constraints with respect to the (compact) support of the given distribution.

• M. Eigel, R. Gruhlke, D. Sommer, Less interaction with forward models in Langevin dynamics: Enrichment and homotopy, SIAM Journal on Applied Dynamical Systems, 23 (2024), pp. 870--1908, DOI 10.1137/23M1546841 .
  Abstract
  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.

• TH. Eiter, R. Lasarzik, Existence of energy-variational solutions to hyperbolic conservation laws, Calculus of Variations and Partial Differential Equations, 63 (2024), pp. 103/1--103/40, DOI 10.1007/s00526-024-02713-9 .
  Abstract
  We introduce 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.

Preprints, Reports, Technical Reports

• P. Hagemann, J. Schütte, D. Sommer, M. Eigel, G. Steidl, Sampling from Boltzmann densities with physics informed low-rank formats, Preprint no. 3153, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3153 .
  Abstract, PDF (2283 kByte)
  Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.

• R. Henrion, G. Stadler, F. Wechsung, Optimal control under uncertainty with joint chance state constraints: Almost-everywhere bounds, variance reduction, and application to (bi-)linear elliptic PDEs, Preprint no. 3151, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3151 .
  Abstract, PDF (92 kByte)
  We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. The controls are deterministic, but the states are probabilistic due to random variables in the governing equation. Joint chance constraints ensure that the random state variable meets pointwise bounds with high probability. For linear governing PDEs and elliptically distributed random parameters, we prove existence and uniqueness results for almost-everywhere state bounds. Using the spherical-radial decomposition (SRD) of the uncertain variable, we prove that when the probability is very large or small, the resulting Monte Carlo estimator for the chance constraint probability exhibits substantially reduced variance compared to the standard Monte Carlo estimator. We further illustrate how the SRD can be leveraged to efficiently compute derivatives of the probability function, and discuss different expansions of the uncertain variable in the governing equation. Numerical examples for linear and bilinear PDEs compare the performance of Monte Carlo and quasi-Monte Carlo sampling methods, examining probability estimation convergence as the number of samples increases. We also study how the accuracy of the probabilities depends on the truncation of the random variable expansion, and numerically illustrate the variance reduction of the SRD.

• V. Aksenov, M. Eigel, An Eulerian approach to the regularized JKO scheme with low-rank tensor decompositions for Bayesian inversion, Preprint no. 3143, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3143 .
  Abstract, PDF (2233 kByte)
  The possibility of using the Eulerian discretization for the problem of modelling high dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to the Wasserstein distance and solved with the entropy-regularized JKO scheme. Each proximal step can be formulated as a fixed-point equation and solved with accelerated methods, such as Anderson's. The usage of the low-rank Tensor Train format allows to overcome the curse of dimensionality, i.e. the exponential growth of degrees of freedom with dimension, inherent to Eulerian approaches. The resulting method requires only pointwise computations of the unnormalized posterior and is, in particular, gradient-free. Fixed Eulerian grid allows to employ a caching strategy, significally reducing the expensive evaluations of the posterior. When the Eulerian model of the target distribution is fitted, the passage back to the Lagrangian perspective can also be made, allowing to approximately sample from the distribution. We test our method both for synthetic target distributions and particular Bayesian inverse problems and report comparable or better performance than the baseline Metropolis-Hastings MCMC with the same amount of resources. Finally, the fitted model can be modified to facilitate the solution of certain associated problems, which we demonstrate by fitting an importance distribution for a particular quantity of interest. We release our code at https://github.com/viviaxenov/rJKOtt.

• R. Lasarzik, E. Rocca, R. Rossi, Existence and weak-strong uniqueness for damage systems in viscoelasticity, Preprint no. 3129, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3129 .
  Abstract, PDF (524 kByte)
  In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, emphweak and emphstrong solutions. For the former, we obtain a global-in-time existence result, but the highly nonlinear character of the system prevents us from proving their uniqueness. For the latter, we prove local-in-time existence. Then, we show that the strong solution, as long as it exists, is unique in the class of weak solutions. This emphweak-strong uniqueness statement is proved by means of a suitable relative energy inequality.

• R. Henrion, D. Hömberg, N. Kliche, Modeling and simulation of an isolated mini-grid including battery operation strategies under uncertainty using chance constraints, Preprint no. 3125, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3125 .
  Abstract, PDF (666 kByte)
  This paper addresses the challenge of handling uncertainties in mini-grid operation, crucial for achieving universal access to reliable and sustainable energy, especially in regions lacking access to a national grid. Mini-grids, consisting of small-scale power generation systems and distribution infrastructure, offer a cost-effective solution. However, the intermittency and uncertainty of renewable energy sources poses challenges, mitigated by employing batteries for energy storage. Optimizing the lifespan of the battery energy storage system is critical, requiring a balance between degradation and operational expenses, with battery operation strategies playing a key role in achieving this balance. Accounting for uncertainties in renewable energy sources, demand, and ambient temperature is essential for reliable energy management strategies. By formulating a probabilistic optimal control problem for minimizing the daily operational costs of stand-alone mini-grids under uncertainty, and exploiting the concept of joint chance constraints, we address the uncertainties inherent in battery dynamics and the associated operational constraints.

• M. Eigel, J. Schütte, Multilevel CNNs for parametric PDEs based on adaptive finite elements, Preprint no. 3124, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3124 .
  Abstract, PDF (2442 kByte)
  A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling best-in-class methods such as low-rank tensor regression in terms of accuracy and complexity. The neural network is trained with data on adaptively refined finite element meshes, thus reducing data complexity significantly. Error control is achieved by using a reliable finite element a posteriori error estimator, which is also provided as input to the neural network. par The proposed U-Net architecture with CNN layers mimics a classical finite element multigrid algorithm. It can be shown that the CNN efficiently approximates all operations required by the solver, including the evaluation of the residual-based error estimator. In the CNN, a culling mask set-up according to the local corrections due to refinement on each mesh level reduces the overall complexity, allowing the network optimization with localized fine-scale finite element data. par A complete convergence and complexity analysis is carried out for the adaptive multilevel scheme, which differs in several aspects from previous non-adaptive multilevel CNN. Moreover, numerical experiments with common benchmark problems from Uncertainty Quantification illustrate the practical performance of the architecture.

• M. Bachmayr, M. Eigel, H. Eisenmann, I. Voulis, A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields, Preprint no. 3112, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3112 .
  Abstract, PDF (3246 kByte)
  The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric variables of solutions. For the corresponding spatial approximations, an independently refined finite element mesh is used for each polynomial coefficient. The method relies on multilevel expansions of input random fields and achieves error reduction with uniform rate. In particular, the saturation property for the refinement process is ensured by the algorithm. The results are illustrated by numerical experiments, including cases with random fields of low regularity.

• D. Hömberg, R. Lasarzik, L. Plato, Existence of weak solutions to an anisotropic electrokinetic flow model, Preprint no. 3104, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3104 .
  Abstract, PDF (729 kByte)
  In this article we present a system of coupled non-linear PDEs modelling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy inequality, via a regularized system. The flow is modelled by a Navier--Stokes--Nernst--Planck--Poisson system and the anisotropy is introduced via space dependent diffusion matrices in the Nernst--Planck and Poisson equation.

Talks, Poster

• L. Plato, Existence and weak-strong uniqueness of suitable weak solutions to an anisotropic electrokinetic flow model, Universität Kassel, Institut für Mathematik, July 18, 2024.

• J. Schütte, M. Eigel, Adaptive multilevel neural networks for parametric PDEs with error estimation, ICLR Workshop on AI4DifferentialEquations In Science, Vienna, Austria, May 11, 2024.

• J. Schütte, Adaptive neural networks for parametric PDEs, Ecole Polytechnique Fédérale de Lausanne, Institut de Mathématiques, Switzerland, October 17, 2024.

• J. Schütte, Approximating Langevin Monte Carlo with resnet-like neural network architectures, 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2024), Session 25.02 ``Various Topics in Computational and Mathematical Methods in Datascience'', March 18 - 22, 2024, Otto-von-Guericke-Universität Magdeburg, March 20, 2024.

• J. Schütte, Bayes for parametric PDEs with normalizing flows, SIAM Conference on Uncertainty Quantification (UQ24), Minisymposium MS37 ``Forward and Inverse Uncertainty Quantification for Nonlinear Problems -- Part II'', February 27 - March 1, 2024, Savoia Excelsior Palace Trieste and Stazione Marittima, Italy, February 27, 2024.

• V. Aksenov, Learning distributions with regularized JKO scheme and low-rank tensor decompositions, Workshop on Optimal Transport from Theory to Applications, Berlin, March 11 - 15, 2024.

• V. Aksenov, Learning distributions with regularized JKO scheme and low-rank tensor decompositions, SIAM Conference on Uncertainty Quantification (UQ24), Minisymposium MS153 ``Low Rank Methods for Random Dynamical Systems and Sequential Data Assimilation -- Part I'', February 27 - March 1, 2024, Savoia Excelsior Palace Trieste and Stazione Marittima, Italy, February 29, 2024.

• V. Aksenov, Modelling distributions with Wasserstein proximal methods and low-rank tensor decompositions, 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2024), Session 15.06 ``UQ -- Sampling and Rare Events Estimation'', March 18 - 22, 2024, Otto-von-Guericke-Universität Magdeburg, March 21, 2024.

• H. Heitsch, Probabilistic maximization of time-dependent capacities in a gas network, Conference ``Mathematics of Gas Transport and Energy'' (MOG 2024), November 10 - October 11, 2024, Regensburg, October 11, 2024.

• CH. Miranda, Functional SDE approximation inspired by a deep operator network architecture, 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2024), Session 25.02 ``Various Topics in Computational and Mathematical Methods in Datascience'', March 18 - 22, 2024, Otto-von-Guericke-Universität Magdeburg, March 19, 2024.

• CH. Miranda, Solving stochastic differential equations using deep operator networks, SIAM Conference on Uncertainty Quantification (UQ24), Minisymposium MS25 ``Nonlinear Approximation of High-Dimensional Functions: Compositional, Low-Rank and Sparse Structures -- Part II'', February 27 - March 1, 2024, Savoia Excelsior Palace Trieste and Stazione Marittima, Italy, February 27, 2024.

• D. Sommer, Approximating Langevin Monte Carlo with ResNet-like neural network architecture (online talk), University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 13, 2024.

• D. Sommer, Approximating Langevin Monte Carlo with resnet-like neural network architectures, SIAM Conference on Uncertainty Quantification (UQ24), Minisymposium MS25 ``Nonlinear Approximation of High-Dimensional Functions: Compositional, Low-Rank and Sparse Structures -- Part II'', February 27 - March 1, 2024, Savoia Excelsior Palace Trieste and Stazione Marittima, Italy, February 27, 2024.

• M. Eigel, Adaptive multilevel neural networks for parametric PDEs with error control, 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2024), Session 15.05 ``Methodologies for Forward UQ'', March 18 - 22, 2024, Otto-von-Guericke-Universität Magdeburg, March 20, 2024.

• M. Eigel, An operator network architecture for functional SDE representations, SIAM Conference on Uncertainty Quantification (UQ24), Minisymposium MS6 ``Operator Learning in Uncertainty Quantification -- Part I'', February 27 - March 1, 2024, Savoia Excelsior Palace Trieste and Stazione Marittima, Italy, February 27, 2024.

• M. Eigel, Generative modelling with tensor compressed HJB approximations, 11th International Conference ``Inverse Problems: Modeling and Simulation'' (IPMS 2024), Minisymposium M7 ``Bayesian, Variational, and Optimization Techniques for Inverse Problems in Stochastic PDEs'', May 26 - June 1, 2024, Paradise-Bay Hotel, Cirkewwa, Malta, May 31, 2024.

• M. Eigel, Sparse and compositional tensor formats for high-dimensional function approximation, Workshop ``High-dimensional Methods in Stochastic and Multiscale PDEs'', September 30 - October 2, 2024, Technische Universität Wien, Austria, October 2, 2024.

• M. Eigel, Topology optimisation under uncertainties, modern tensor compression & empirical SFEM, UQ Colloquium, Bosch Research Campus, Renningen, October 11, 2024.

• R. Henrion, D. Hömberg, N. Kliche, Optimal operation of mini-grids including battery management under uncertainty, 5. Workshop ``Women in Optimization 2024'', Friedrich-Alexander-Universität Erlangen, April 10 - 12, 2024.

• R. Henrion, D. Hömberg, N. Kliche, Optimal operation of mini-grids including battery management under uncertainty, Summer School ``Data-driven Dynamical Systems'', Universität Bremen, July 24 - 26, 2024.

• R. Henrion, An enumerative formula for the spherical cap discrepancy, PGMO DAYS 2024, Session 11E ``Stochastic and Robust Optimization'', November 19 - 20, 2024, Gaspard Monge Program for Optimization, Operations Research and their Interaction with Data Science, EDF Lab Paris-Saclay, Palaiseau, France, November 20, 2024.

• R. Henrion, An introduction to chance-constrained programming, Summer School on Optimization, Uncertainty, and AI, Hamburg, August 9, 2024.

• R. Henrion, Chance constraints in energy management and aspects of nonsmoothness, Workshop ``Variational Analysis and Applications for Modeling of Energy Exchange'' (VAME 2024), May 13 - 14, 2024, Universität Trier, May 13, 2024.

• R. Henrion, On a chance-constrained optimal control problem with turnpike property, 3rd International Conference on Variational Analysis and Optimization, January 16 - 19, 2024, Universidad de Chile, Santiago, Chile, January 16, 2024.

• R. Henrion, Optimization problems with probabilistic/robust (probust) constraints: Theory, numerics and applications, FIP TC 7 Conference on System Modeling and Optimization, August 12 - 16, 2024, Hamburg, August 12, 2024.

• D. Hömberg, Two-scale topology optimization -- Modeling, analysis and numerical results, XIV International Conference of the Georgian Mathematical Union, September 2 - 7, 2024, Batumi Shota Rustaveli State University, Georgia, September 3, 2024.

• R. Lasarzik, Energy-variational solutions for different viscoelastic fluid models, Conference ``Mathematics of Fluids in Motion: Recent Results and Trends'', November 11 - 15, 2024, Centre International de Rencontres Mathematiques (CIRM), Marseille, France, November 11, 2024.

• R. Lasarzik, Evolutionary variational inequalities as generalized solution concepts, Università degli Studi di Pavia, Dipartimento di Matematica, Italy, November 27, 2024.

• R. Lasarzik, Minimizing movements for damped Hamiltonian systems, Workshop on Optimal Transport from Theory to Applications, Berlin, March 11 - 15, 2024.

• R. Lasarzik, Phase separation in a viscoelastoplastic fluid model in geophysics, International Conference on Free Boundary Problems: Theory and Application (FBP 2024), August 26 - 30, 2024, João Pessoa City, Brazil, August 27, 2024.

• A. Rathsfeld, Analysis of scattering matrix algorithm for diffraction by periodic structures (online talk), University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 13, 2024.

External Preprints

• M. Eigel, J. Schütte, Adaptive multilevel neural networks for parametric PDEs with error estimation, Preprint no. arXiv:2403.12650, Cornell University, 2024, DOI 10.48550/arXiv.2403.12650 .