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Monday, 15.04.2024, 14:00 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Anthony Nouy, Ecole Centrale de Nantes, Frankreich:
Moment methods for some optimal transport problems and parameter-dependent equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Most optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. Another route is to approximate moments of measures, when these are determinate. Here, we show that many common OT problems can be formulated as generalized moment problems [1]. These include the computation of Lp Wasserstein or Gromov-Wasserstein distances and the corresponding barycenters. For measures supported on compact semi-algebraic sets, a practical numerical approach then consists in truncating moment sequences up to a certain order, and using the polynomial sums-of-squares hierarchy. The approach is proved to converge. It allows to extract a posteriori relevant information on the measures, such as their supports that can be estimated using Christoffel-Darboux kernels. In a second part of this talk, we present how these moment methods can be used for the solution of parameter-dependent hyperbolic equations, by using weak formulations on measure-valued solutions [2]. These methods can be used to directly approximate the solution as a function of the parameter, or to construct reduced order models by interpolation in Wasserstein spaces.

These are joint works with Olga Mula and Clément Cardoen, Swann Marx and Nicolas Seguin.


References:

[1] O. Mula and A. Nouy. Moment-SoS methods for optimal transport problems, arXiv:2211.10742, 2022.

[2] C. Cardoen, S. Marx, A. Nouy, and N. Seguin. A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws, 2024.

Host
WIAS Berlin

Tuesday, 16.04.2024, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Apala Majumdar, University of Strathclyde, GB:
Solution landscapes in the Landau-de Gennes theory for nematic liquid crystals: Analysis, computations and applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Nematic liquid crystals are classical examples of partially ordered materials that combine fluidity with the order of crystalline solids. They are the working material of a range of electro-optic devices i.e. in the liquid crystal display industry and more recently, they are used in sensors, actuators, elastomers, security applications and pathological studies. We review the celebrated Landau-de Gennes theory for nematic liquid crystals and focus on the modelling of nematics confined to thin quasi-2D systems, with reference to 2D polygons. We perform asymptotic analysis in certain distinguished limits, encoded in terms of geometrical, material and temperature-dependent parameters, accompanied by exhaustive numerical studies of solution landscapes that include stable and unstable solution branches for these systems. There are several numerical challenges associated with the numerical computation of the unstable solution branches and their unstable directions, for which we use the powerful High-Index Shrinking Optimisation Dimer Method. In the last leg of the talk, we discuss the mathematical modelling of some recent experiments on nematic shells and doped bent-core liquid crystals, to illustrate the synergistic links between theory, experiment and novel applications.

All collaborations will be acknowledged throughout the talk.

Host
WIAS Berlin

Tuesday, 16.04.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Maalvladedon Ganet Some, University of Ghana, Republik Ghana:
Stochastic optimal control of a prosumer in a district heating system
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We consider networks of residential heating systems in which several prosumers satisfy their heating and hot water demand using solar thermal collectors and services of a central producer. Overproduction of heat can either be stored in a local thermal storage or sold to the network. Our focus is the minimization of the prosumers expected total cost from purchasing and selling thermal energy and running the system. This decision making problem under uncertainty about the future production and consumption of thermal energy is formulated as a stochastic optimal control problem and solved with dynamic programming techniques. We present numerical results for the value function and the optimal control.

Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 17.04.2024, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Gil Kur, ETH Zürich, Switzerland:
Connections between minimum norm interpolation and local theory of Banach spaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 17.04.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
Curvature effects in pattern formation: Analysis and control of a sixth-order Cahn--Hilliard equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, the well-posedness and optimal control are discussed for a sixth-order Cahn--Hilliard system, which represents a higher-order variant of the well-known Cahn--Hilliard equation. In our system, the evolution equation is complemented with a source term, where the control variable enters as a distributed mass regulator. The presence of further spatial derivatives in the sixth-order formulation enables the model to capture curvature effects, for a more accurate description of isothermal phase separation dynamics in complex materials systems. A well-posedness result for the initial-boundary value problem is shown when assuming a smooth double-well potential as part of the free energy. Then, the related optimal control problem is addressed. Existence of optimal controls is established, and the first-order necessary optimality conditions are characterized via a suitable variational inequality involving the solution to the adjoint problem. These results have been obtained in a recent collaboration with G. Gilardi (University of Pavia), A. Signori (Polytechnic of Milan) and J. Sprekels (WIAS Berlin).

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
Monday, 22.04.2024, 13:30 (WIAS-ESH)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Johannes Royset, University of Souther California, USA:
Approximations of Rockafellians, Lagrangians, and Dual Functions. The case for solving surrogates instead of actual optimization problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Optimization problems are notorious for being unstable in the sense that small changes in their parameters can cause large changes in solutions. However, Rockafellian relaxations, Lagrangian relaxations, and dual problems are typically more stable. While focusing on the nonconvex case, we develop sufficient conditions under which approximations of Rockafellian relaxations, Lagrangian relaxations, and dual problems convergence, epigraphically or hypographically, to limiting counterparts, and quantify the rate of convergence. The conditions are milder than those required by approximations of the actual problems confirming the importance of these surrogate problems. We illustrate the results in the context of composite problems, stochastic optimization, and Rockafellians constructed by augmentation.

Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems

Host
WIAS Berlin
Tuesday, 23.04.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. John Schoenmakers, WIAS Berlin:
Optimal stopping with randomly arriving opportunities to stop
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 24.04.2024, 11:30 (WIAS-405-406)
Seminar Interacting Random Systems
Julia Hörmann, WIAS Berlin:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Wednesday, 24.04.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Ruming Zhang, Technische Universität Berlin:
Direct and inverse problems in periodic waveguides
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Waveguides play important roles in many application areas, for example, in communications. An essential topic in the development of modern techniques is based on the deep understanding of the behaviours of the waves propagating in the waveguides. Then, numerical methods are proposed to simulate the physical processes and mathematical methods are developed to solve the related inverse problems. In this talk, I will first focus on the direct problem, that is study the timeharmonic wave propagating in the periodic waveguide both analytically and numerically. The problem is modeled by the Helmholtz equation in a periodic strip. Afterwards, I will also introduce one example of the solution to an inverse problem.

Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Tuesday, 30.04.2024, 10:15 (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Igor Voulis, Georg-August-Universität Göttingen:
An adaptive stochastic FEM method for the Poisson problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Tuesday, 14.05.2024, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Thomas Möllenhoff, RIKEN Center for Advanced Intelligence Project, Japan:
Variational learning for large deep networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We present extensive evidence against the common belief that variational Bayesian learning is ineffective for large neural networks. First, we show that a popular deep learning method called sharpness-aware minimization (SAM) solves an optimal relaxation of the variational Bayesian objective. Then, we demonstrate that a direct optimization of the variational objective with an Improved Variational Online Newton method (IVON) can consistently match or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of variational learning where we improve fine-tuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence in support of effectiveness of variational methods for deep learning.

Further Informations
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 22.05.2024, 14:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jürgen Sprekels, WIAS Berlin:
Necessary and sufficient optimality conditions in the sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Host
Humboldt-Universität zu Berlin
WIAS Berlin
July 1, 2024 (WIAS-ESH)
Workshop/Konferenz: Developments in Computational Finance - Honoring John Schoenmakers on the occasion of his retirement
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin