Upcoming Events
Many events are currently organized online. Information on how to access these events can be found by clicking “more” below the respective entry.
- Wednesday, 22.03.2023, 10:00 (WIAS-406)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Constantin Christof, Technische Universität München:
On the identification and optimization of nonsmooth superposition operators in semilinear elliptic PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
We study an infinite-dimensional optimization problem that aims to identify the Nemytskii operator in the nonlinear part of a prototypical semilinear elliptic partial differential equation which minimizes the distance between the PDE-solution and a given desired state. In contrast to previous works, we consider this identification problem in a low-regularity regime in which the function inducing the Nemytskii operator is a-priori only known to be an element of H1loc. This makes the studied problem class a suitable point of departure for the rigorous analysis of training problems for learning-informed PDEs in which an unknown superposition operator is approximated by means of a neural network with nonsmooth activation functions (ReLU, leaky-ReLU, etc.). We establish that, despite the low regularity of the controls, it is possible to derive a classical stationarity system for local minimizers and to solve the considered problem by means of a gradient projection method. It is also shown that the established first-order necessary optimality conditions imply that locally optimal superposition operators share various characteristic properties with commonly used activation functions: They are always sigmoidal, continuously differentiable away from the origin, and typically possess a distinct kink at zero.
Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Host
WIAS Berlin
- Thursday, 23.03.2023, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, UK:
Positivity-preserving discretisations in general meshes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The quest for physical consistency in the discretisation of PDEs started as soon as the numerical methods started being proposed. By physical consistency we mean a discretisation that by design satisfies a property also satisfied by the continuous PDE. This property might be positivity of the discrete solution, or preservation of some bounds (e.g., concentrations should belong to the interval [0, 1]), or can also be energy preservation, or exactly divergence-free velocities for incompressible fluids. Regarding positivity preservation, this topic has been around since the pioneering work by Ph. Ciarlet in the late 1960s and early 1970s. In the context of finite element methods, it was shown in those early works (and not significantly improved since), that in order for a finite element method to preserve positivity the mesh needs to satisfy certain geometrical restrictions, e.g., in two space dimensions with simplicial elements the triangulation needs to be of Delaunay type (in higher dimensions or quadrilateral meshes the restrictions are more involved). Throughout the years several conclusions have been reached in this topic, but in the context of finite element methods the discretisations tend to be of first order in space. So, many important problems still remain open. In particular, one open problem is how to build a discretisation that will lead to a positive solution regardless of the geometry of the mesh and the order of the finite element method. In this talk I will review recent results addressing the last question posed in the last paragraph. More precisely, I will present a method that enforces bound-preservation (at the degrees of freedom) of the discrete solution. The method is built by first defining an algebraic projection onto the convex closed set of finite element functions that satisfy the bounds given by the solution of the PDE. Then, this projection is hardwired into the definition of the method by writing a discrete problem posed for this projected part of the solution. Since this process is done independently of the shape of the basis functions, and no result on the resulting finite element matrix is used, then the outcome is a finite element function that satisfies the bounds at the degrees of freedom. Another important observation to make is that this approach is related to variational inequalities, and this fact will be exploited in the error analysis. The core of the talk will be devoted to explaining the main idea in the context of linear (and nonlinear) reaction-diffusion equations. Then, I will explain the main difficulties encountered when extending this method to convection-diffusion equations, and, more importantly, to a finite element method defined in polytopal meshes. The results in this talk have been carried out in collaboration with Abdolreza Amiri (Strathclyde, UK), Emmanuil Geourgoulis (Heriot-Watt, UK and Athens, Greece), Tristan Pryer (Bath, UK), and Andreas Veeser (Milan, Italy).
Further Informations
Seminar Numerische Mathematik
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 23.03.2023, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Lutz Mertenskötter, WIAS Berlin:
Laser linewidth estimation beyond the detector noise limit - Statistical inference from delayed self-heterodyne measurements
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Forschungsseminar Mathematische Modelle der Photonik
Host
WIAS Berlin
- Friday, 24.03.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Heike Sill, WIAS:
Kosten-Leistungs-Rechnung (KLR) am WIAS
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Further Informations
hybrid event
Host
WIAS Berlin
- Tuesday, 04.04.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Robert A. Vandermeulen, TU Berlin:
Beating the nonparametric curse of dimensionality using multi-view density estimators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The curse of dimensionality is a famous statistical phenomenon that is perhaps nowhere better exemplified than in the task of nonparametric density estimation. Here the curse of dimensionality is not only evident in practical applications, but there is a very robust corpus of theoretical work that demonstrate the curse of dimensionality. This talk will cover recent work on nonparametric density estimation that utilizes multi-view models, which are a type of low-rank model, to obviate the curse of dimensionality and give dimension-independent rates of convergence.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Monday, 17.04.2023, 10:00 (ATB)
- Leibniz MMS Days
Leibniz MMS Days 2023
more ... Location
Agricultural Engineering and Bioeconomy Potsdam
Host
Leibniz Institute for Agricultural Engineering and Bioeconomy
WIAS Berlin
- Wednesday, 19.04.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Properties of recursive trees with independent fitnesses
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We study a general model of recursive trees, where nodes are equipped with random weights, arrive one at a time, and connect to existing nodes with probability proportional to a general function of their degree and their weight. We study the limiting infinite tree associated with this model, and show that, under a certain 'explosive' regime, the limiting tree has only a single node of infinite degree, or a single infinite path. We provide sufficient criteria to determine which occurs. Based, in part, on joint work with Bas Lodewijks.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 19.04.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Leon Schütz, WIAS Berlin:
An existence theory for solitary waves on a ferrofluid jet (hybrid talk)
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
- Wednesday, 26.04.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
The Cahn--Hilliard--Oono system with control in the mass term (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The problem of optimal control for the Cahn--Hilliard--Oono system is addressed, where the control u is located in the mass term. First, well-posedness of the problem and the dependence of the phase variable on the control u are considered, all this by admitting general potentials that include both the case of regular potentials and the case of some singular potential. Next, the so-called separation property is discussed: it holds for everywhere defined regular potentials in 2D and 3D and for the logarithmic potential in 2D. Finally, in this framework, for the control problem it is shown that an optimal control exists; the control-to-state map is Frechet differentiable; a proper variational inequality involving the solution of an adjoint system is a necessary condition for optimality. The results reported in this talk have been obtained in a collaboration with G. Gilardi, E. Rocca and J. Sprekels.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 03.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Luisa Andreis, Politecnico di Milano, Italien:
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, 10.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, 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
- Tuesday, 16.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Christian Hirsch, Aarhus University, Dänemark:
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, 17.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Clément Erignoux, INRIA Lille, Frankreich:
Symmetric and asymmetric hydrodynamics for the facilitated exclusion process via mapping
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The facilitated exclusion process is a degenerate kinetically constrained lattice gas, in which particles can hop to an empty neighboring site provided that another neighboring site is also occupied. Because of the kinetic constraint, the system in dimension 1 exhibits two phases, a frozen phase at density less than 1/2, and a diffusive phase at density larger than 1/2. For this reason, standard entropic tools cannot be used to straightforwardly derive its macroscopic behavior, in particular its hydrodynamic limit. To workaround this issue, we exploit a classical mapping between exclusion and zero-range processes, and deduce from the hydrodynamic limit of the zero-range process that of the exclusion process. Despite the lack of smoothness of the various macroscopic limits, thanks to the attractiveness of the zero-range process, this allows to derive the hydrodynamic limits in both the symmetric and asymmetric case. Based on JW With O. Blondel, M. Sasada, M. Simon and L. Zhao
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 24.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Renato Soares dos Santos, Universidade Federal de Minas Gerais (UFMG), Brasilien:
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, 07.06.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Günter Last, Karlsruher Institut für Technologie:
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
- July 3 – 5, 2023 (WIAS-ESH)
- Workshop/Konferenz: Nonlinear Dynamics in Semiconductor Lasers 2023
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik
WIAS Berlin
- Friday, 07.07.2023, 08:00 (Harnack-Haus)
- Workshop: Phase transitions in random point systems
Phase transitions in random point systems
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
- Monday, 17.07.2023, 09:00 (Harnack-Haus)
- SPP2265 Summer School: Probability and geometry on configuration spaces
SPP2265 Summer School: Probability and geometry on configuration spaces
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
- August 30 – September 1, 2023 (WIAS-ESH)
- Workshop/Konferenz: Workshop on Biophysics-based modeling and data assimilation in medical imaging 2023
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
Charité - Universitätsmedizin Berlin
- September 13 – 15, 2023 (WIAS-ESH)
- Workshop/Konferenz: Energetic Methods for Multi-Component Reactive Mixtures Modelling Stability and Asymptotic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The central theme of this workshop are mechanical models describing the transport of mass, momentum, and energy in multi-component mixtures, including diffusion, convection, and heat transfer. A consistent account of reactions is a further concern. EMRM 2023 focuses in particular on energetic and entropic tools for strongly coupled systems of hyperbolic--parabolic type, whose analysis is still underdeveloped and has received insufficient attention relative to their tremendous significance in real-world applications. Many complex physical processes not only involve mass transfer induced by random diffusion, but also reaction processes and directed transport including non-local drifts induced, for instance, by the interaction of electrically charged particles. The relative influence of these different processes will depend on the specific application. Developing a framework that asymptotically relates the different models is nowadays an active field of research in multi-component flow modelling. This workshop focuses on the analysis of multi-component mixtures using diffusion models and hydrodynamic models, on the analysis of complex evolutionary systems of hyperbolic--parabolic type, including multi-phase problems, as well as on the connections between these approaches by means of asymptotic analysis.
Host
WIAS Berlin
Technische Universität Wien