Upcoming Events
- Wednesday, 08.01.2025, 10:00 (WIAS-HVP-3.13)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Johannes Schmidt-Hieber, University of Twente:
Statistical stimation using zeroth-order optimization
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstract
In this talk, we study statistical properties of zeroth-order optimization schemes, which do not have access to the gradient of the loss and rely solely on evaluating the loss function. Such methods are often considered to be suboptimal for high-dimensional problems, as their convergence rates to the minimizer of the objective function are typically slower than those of gradient-based methods. This performance gap becomes more pronounced as the number of parameters increases. Considering the linear model, we show that reusing the same data point for multiple zeroth-order updates can overcome the gap in the estimation rates. Additionally, we demonstrate that zeroth-order optimization methods can achieve the optimal estimation rate when only queries from the linear regression model are available. Special attention will be given to the non-standard minimax lower bound in the query model. This is joint work with Thijs Bos, Niklas Dexheimer and Wouter Koolen.
Further Informations
Dieser Vortrag findet hybrid statt. Die Teilnahme per Zoom ist über den (neuen!) Link: https://hu-berlin.zoom-x.de/j/62476510180?pwd=1bws9DORlDM2Iub3ANrb7zzDNANvsJ.1
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Wednesday, 08.01.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Peter Gracar, University of Leeds:
Lipschitz cutset for fractal graphs and applications to the spread of infections
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
For Bernoulli supercritical percolation on the $d$-dimensional lattice it is well understood that the infinite component exists ?everywhere?. In fact, it can be shown that this component contains as a subset a Lipschitz connected hyper-surface that can be built along any of the $d-1$ possible canonical hyperplanes of $mathbbZ^d$. In this talk, we will explain how one can construct a set satisfying similar properties on the Sierpiński gasket and then show how a multi-scale construction can be used to get its existence even for particle dependent percolation. More precisely, we will consider the fractal Sierpiński gasket or carpet graph in dimension $dgeq 2$, denoted by $G$. At time $0$, we place a Poisson point process of particles onto the graph and let them perform independent simple random walks, which in this setting exhibit sub-diffusive behaviour. We will generalise the concept of particle process dependent Lipschitz percolation to the (coarse graining of the) space-time graph $Gtimes mathbbR$, where the opened/closed state of space-time cells is measurable with respect to the particle process inside the cell. We will discuss an application of this generalised framework through the following: if particles can spread an infection when they share a site of $G$, and if they recover independently at some rate $gamma>0$, then if $gamma$ is sufficiently small, the infection started with a single infected particle survives indefinitely with positive probability.
Host
WIAS Berlin
- Wednesday, 08.01.2025, 15:15 (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
Estimates for operator functions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In several branches of mathematics and mathematical physics estimates for operator functions are of high interest. On one hand, this is the case in quantum chemistry, in particular in the analysis of the Kohn--Sham system. Here we present an elementary proof of the Birman--Solomyak theorem - which was an open problem for a long time. The second item of the talk affects operator functions for second order divergence operators. We give an impoved estimate for the angle of the sector which contains the numerical range and draw several consequences of this.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- January 13, 2025 (WIAS-Library)
- Workshop/Konferenz: MATh.en.JEANS - Workshop von und für Schüler:innen
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Monday, 13.01.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Markus Pappik, Hasso Plattner Institute:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Tuesday, 14.01.2025, 13:30 (WIAS-405-406)
- Seminar Numerische Mathematik
Prof. Dr. Jinchao Xu, King Abdullah University of Science and Technology:
Finite neuron methods for partial differential equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this talk, I will report several theoretical and numerical studies of finite neuron method for partial differential equations. Topics include approximation properties of neural network functions, error estimates for the finite neuron method, convergence analysis of training algorithms, the relationship between ReLU^k finite neuron method with the tradition finite element and spectral method, and the comparison of their efficiency for high dimensional problems.
Host
WIAS Berlin
- Wednesday, 15.01.2025, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Xiaorui Zuo, National University of Singapore:
Cryptos have rough volatility and correlated jumps
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Dieser Vortrag findet hybrid statt. Die Teilnahme per Zoom ist über den (neuen!) Link: https://hu-berlin.zoom-x.de/j/62476510180?pwd=1bws9DORlDM2Iub3ANrb7zzDNANvsJ.1
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Wednesday, 15.01.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Riccardo Michielan, University o Twente:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 15.01.2025, 15:15 (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Patrik Knopf, Universität Regensburg:
The Cahn--Hilliard equation with dynamic boundary conditions and its application to two-phase flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The Cahn--Hilliard equation is the most common model to describe phase separation processes in a mixture of two materials. Moreover, it is further used to describe different phenomena where the distribution and/or motion of two (or more) immiscible materials is considered. Standard Cahn--Hilliard models are usually endowed with homogeneous Neumann boundary conditions for both the phase-field variable and the chemical potential. However, these boundary conditions yield certain limitations: 1.) The diffuse interface separating the materials is enforced to intersect the boundary at a perfect angle of ninety degrees, which is unrealistic in many applications. 2.) No transfer of material between bulk and boundary is allowed and thus, absorption process cannot be described. For these reasons dynamic boundary conditions for the Cahn--Hilliard equation have been introduced. We take a closer look at dynamic boundary conditions that also exhibit a Cahn--Hilliard type structure. To describe the evolution of two-phase flows, Navier--Stokes--Cahn--Hilliard models have become a popular choice. As the standard models are subject to a no-slip boundary condition for the velocity field as well as homogeneous Neumann conditions for the Cahn--Hilliard subsystem, they exhibit the aforementioned limitations and are also not well-suited for describing general moving contact line phenomena. However, these issues can also be overcome by the introduction of suitable dynamic boundary conditions.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 22.01.2025, 14:00 (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jan-Frederik Pietschmann, Universität Augsburg:
Gradient flows on metric graphs with reservoirs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We study an evolution equation on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store mass. We focus on the case then the dynamics is driven by an entropy functional, defined both on edges and vertices. We provide a rigorous understanding of such equations as a gradient flow (in continuity equation format) with respect to metric that allows for a coupling between edge and vertex dynamics. By approximating the edges by a sequence of vertices, resulting in a fully discrete system, we are able to establish existence of solutions in this formalism. Next, we study several scaling limits and using in the framework of EDP convergence with embedding we are able to rigorously show convergence to again gradient flows on reduced graphs. Finally, numerical studies confirm our theoretical findings.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- January 29 – 31, 2025 (WIAS-405-406)
- Workshop/Konferenz: Critical behaviour in spatial particle systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 29.01.2025, 10:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Anh Duc Vu, WIAS Berlin:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 12.02.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Benedikt Jahnel, WIAS Berlin and TU Braunschweig:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin