Veranstaltungen

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Dienstag, 22.10.2019, 15:00 Uhr (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Regularization by noise for SDEs and SPDEs with applications to numerical methods
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
WIAS Berlin
Mittwoch, 23.10.2019, 10:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Vladimir Spokoiny, WIAS Berlin, HU Berlin:
Bayesian inference for nonlinear inverse problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We discuss the properties of the posterior for a wide class of statistical models including nonlinear generalised regression and deep neuronal networks, nonlinear inverse problems, nonparametric diffusion, error-in-operator and IV models. The new calming approach helps to treat all such problems in a unified manner and to obtain tight finite sample results about Gaussian approximation of the posterior with an explicit error bound in term of so called effective dimension.

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 23.10.2019, 11:00 Uhr (WIAS-HVP-3.13)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Martin Holler, Universität Graz, Österreich:
A variational model for learning convolutional image atoms from incomplete data
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
Using lifting and relaxation strategies, we present a convex variational model for learning a convolutional sparse representation of image data via a few basic atoms. Such a representation provides a model for repeating patterns, but is also of interest for classification or as structural prior. We ensure well-posedness results for the proposed model in a general inverse problems setting and provide numerical experiments, where an atom-based representation is computed from incomplete, noisy and blurry data.

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Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 23.10.2019, 14:00 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Ansgar Jüngel, Technische Universität Wien, Österreich:
Cross-diffusion systems: from spin semiconductors to biological populations with stochastic forcing
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Many real-world applications consist of multiple components, leading on the macroscopic scale to cross-diffusion systems which consist of strongly coupled parabolic equations. The applications may be very diverse and range from spin-polarized transport in semiconductors and ion transport in cell membranes to population dynamics. In this talk, some existence results for global-in-time weak solutions is proved, based on entropy methods. This technique was already used by Herbert Gajewski, and we detail some of his ideas to prove the large-time behavior and uniqueness of weak solutions, followed by some extensions like boundedness-by-entropy and martingale solutions to stochastic cross-diffusion systems.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 30.10.2019, 11:30 Uhr (WIAS-406)
Seminar Interacting Random Systems
Dr. Niccolo Torri, Université Paris Nanterre, Frankreich:
Directed polymer in a heavy-tail random environment
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
A classical problem in the field of disordered systems is to understand the behaviour of a directed polymer in interaction with a random environment. Mathematically, the directed polymer is modeled by a directed random walk and the random environment is a sequence of random variables which can interact with the random walk perturbing its behaviour, giving rise to super-diffusive transversal fluctuations and localisation phenomena. Understanding the typical trajectories of the the walk is a very challenging issue and several results have been obtained when the random environment has exponential moments. In this talk we consider the case of a heavy-tail random environment, that is, the environment?s distribution function decades polynomially with exponent $alpha >0$. We mainly focus on the case in which the random environment has no second moment ($alphain (0,2)$), finding the super-diffusive transversal fluctuations of the polymer as function of the parameter $alpha$. Joint work with Quentin Berger (Sorbonne Université).

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Seminar Interacting Random Suystems

Veranstalter
WIAS Berlin
Mittwoch, 30.10.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Katharina Hopf, WIAS Berlin:
On the singularity formation and relaxation to equilibrium in 1D Fokker--Planck model with superlinear drift
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 31.10.2019, 14:00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Prof. Max Gunzburger, Florida State University, USA:
Four “better” ways to solve the Navier--Stokes equations: Simulation of Richardson pair dispersion, ensemble discretization methods, an auxiliary equation approach for UQ, and filtered regularizations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The facetious and self-serving title refers to four approaches for Navier-Stokes simulations. The first involves the analysis, numerical analysis, and an efficient implementation strategy for a recently proposed fractional Laplacian closure model that accounts for Richardson pair dispersion observed in turbulent flows. The second is the exploitation of accurate and widely applicable ensemble methods in settings in which multiple inputs need to be processed, as may be the case for uncertainty quantification, reduced-order modeling, and control and optimization. The third addresses the lack of regularity of solutions and the resultant loss of accuracy of approximations in the case of white or weakly correlated additive noise forcing. The fourth involves filtered spectral viscosity and hierarchical finite element methods for regularized Navier-Stokes equations.

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Institutskolloquium

Veranstalter
WIAS Berlin
Donnerstag, 31.10.2019, 16:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Jan-Philipp Köster, Ferdinand-Braun-Institut Berlin:
Traveling wave model based simulation of tunable multi-wavelength diode laser and MOPA systems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Freitag, 01.11.2019, 14:00 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Ana Djurdjevac, FU Berlin, Institut für Mathematik:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
tba

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Montag, 04.11.2019, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Christopher Rackauckas, Massachusetts Institute of Technolog/University of Maryland, USA:
Neural differential equations as a basis for scientific machine learning
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Scientific Machine Learning (SciML) is an emerging discipline which merges the mechanistic models of science and engineering with non-mechanistic machine learning models to solve problems which were previously intractable. Recent results have showcased how methods like Physics Informed Neural Networks (PINNs) can be utilized as a data-efficient learning method, embedding the structure of physical laws as a prior into a learnable structures so that small data and neural networks can sufficiently predict phenomena. Additionally, deep learning embedded within backwards stochastic differential equations has been shown to be an effective tool for solving high-dimensional partial differential equations, like the Hamilton-Jacobian-Bellman equation with 1000 dimensions. In this talk we will introduce the audience to these methods and show how these diverse methods are all instantiations of a neural differential equation, a differential equation where all or part of the equation is described by a latent neural network. Once this is realized, we will show how a computational tool, DiffEqFlux.jl, is being optimized to allow for efficient training of a wide variety of neural differential equations, explaining how the performance properties of these equation differ from more traditional uses of differential equations and some of the early results of optimizing for this domain. The audience will leave knowing how neural differential equations and DiffEqFlux.jl may be a vital part of next-generation scientific tooling.

Veranstalter
WIAS Berlin
Donnerstag, 14.11.2019, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Benoît Gaudeul, Université de Lille , Frankreich:
Some numerical schemes for a reduced case of a Nernst--Planck--Poisson model
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We compare several di erent numerical strategies to simulate a Nernst--Planck--Poisson model introduced in [1]. Different equivalent formulations are exploited based either on concentrations or activities [2]. As a first step, we focus on a simplified model for ionic liquid, for which four different schemes are discussed. A particular attention is given to the preservation at the discrete level of key features of the continuous problem, that are the positivity of the concentrations and the dissipation of the energy along time. The existence and convergence of a discrete solutions to the nonlinear system corresponding to each scheme is then established. Finally, numerical comparisons between the schemes are provided.

References
[1] Wolfgang Dreyer, Clemens Guhlke, and Rüdiger Müller. Overcoming the shortcomings of the Nernst--Planck model. Physical Chemistry Chemical Physics, 15, 2013.
[2] Jürgen Fuhrmann. Comparison and numerical treatment of generalised Nernst--Planck models. Computer Physics Communications, 6, 2015.

Veranstalter
WIAS Berlin
Mittwoch, 20.11.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Antonius Frederik Maria ter Elst, The University of Auckland, Neuseeland:
The Dirichlet-to-Neumann operator on C 1+κ -domains
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We present some recent results on kernel bounds for the semigroup generated by the Dirichlet-to-Neumann operator when the underlying operator has Hölder continuous coefficients and the domain has a C 1+κ-boundary. The proof depends on Gaussian bounds for derivatives of the semigroup kernel of an elliptic operator with Dirichlet boundary conditions. As a consequence the Dirichlet-to-Neumann semigroup is holomorphic on the right half-plane on L¹. Moreover, it is also strongly continuous on the space of continuous functions on the boundary and holomorphic on the right half-plane.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 21.11.2019, 11:00 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Jo Brüggemann, WIAS:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
tba

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin