Upcoming Events
- Tuesday, 01.07.2025, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Helena Kremp, WIAS Berlin:
Overcoming the order barrier for approximations of nonlinear SPDEs with additive space-time white noise
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 02.07.2025, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Merle Munko, Otto-von-Guericke-Universität Magdeburg:
Multiple tests for mean functions of functional data
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs for comparing different groups or inferring factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both univariate and multivariate mean functions without assuming particular error distributions or homoscedasticity. That is, we allow for different structures of the covariance functions between groups. We analyse the (joint) asymptotic behaviour of suitable test statistics and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotically valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and Finally illustrate their applicability by analysing a data set. Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs for comparing different groups or inferring factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both univariate and multivariate mean functions without assuming particular error distributions or homoscedasticity. That is, we allow for different structures of the covariance functions between groups. We analyse the (joint) asymptotic behaviour of suitable test statistics and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotically valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and finally illustrate their applicability by analysing a data set.
Further Informations
Dieser Vortrag findet hybrid statt. Die Teilnahme per Zoom ist über den (neuen!) Link:
https://hu-berlin.zoom-x.de/j/64809417303?pwd=iLT5xbdDZspAcUCuLrwNnaN90ZQBpj.1
Meeting-ID: 648 0941 7303
Passwort: 258449
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Wednesday, 02.07.2025, 11:00 (WIAS-Library)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Eleonora Ficola, Universität Hamburg:
Existence and duality theory for linear-growth variational problems with measures
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstract
We consider functionals F with linear growth in the gradient variable coupled with a non-linear integral term respect to a (possibly signed) Radon measure on bounded domains in Rn. After achieving a generalized parametric lower-semicontinuity result, we then provide necessary and sufficient conditions for existence of BV-minimizers of F, discussing typical examples as well as limit cases. In parallel, we determine the corresponding dual maximization problem set in the class of divergence-measure vector fields and we reformulate the optimality relations in terms of a refined version of Anzellotti's pairing between measures and functions. By introducing a suitable notion of solutions to the Euler-Lagrange equation associated to F, we then demonstrate that our BV theory is complete and it provides natural extension to the Sobolev model. The seminar is based on joint work with Thomas Schmidt (Universität Hamburg).
Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Host
WIAS Berlin
- Wednesday, 02.07.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Jonas Köppl, WIAS Berlin:
Two edges suffice: the planar lattice two-neighbor graph percolates
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The $k$-neighbor graph is a directed percolation model on the hypercubic lattice $Z^d$ in which each vertex independently picks exactly $k$ of its $2d$ nearest neighbors at random, and we open directed edges towards those. We prove that the $2$-neighbor graph percolates on $Z^2$, i.e., that the origin is connected to infinity with positive probability. The proof rests on duality, an exploration algorithm, a comparison to i.i.d. bond percolation under constraints as well as enhancement arguments. As a byproduct, we show that i.i.d. bond percolation with forbidden local patterns has a strictly larger percolation threshold than $1/2$. Additionally, our main result provides further evidence that, in low dimensions, less variability is beneficial for percolation.
Host
WIAS Berlin
- Wednesday, 02.07.2025, 14:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Benjamin Gess, TU Berlin & MPI Leipzig:
From large deviations around porous media, to PDEs with irregular coefficients, to gradient flow structures
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider the large deviations of the rescaled zero-range process about its hydrodynamic limit, the porous medium equation. This leads to a variational characterization of solutions to the porous medium equation, and to the analysis of the skeleton equation, an energy-critical, degenerate PDE with irregular drift. We then present a robust well-posedness theory for such PDEs based on concepts of renormalized solutions, the equation's kinetic form, and commutator estimates. The relationship of such large deviations principles to a gradient flow interpretation of the porous medium equation will be demonstrated by deducing an entropy dissipation equality from the large deviations and reversibility.
Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- July 3 – 5, 2025 (WIAS-ESH)
- Workshop/Konferenz: 21st Annual Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Technische Universität Berlin
University of Oxford
WIAS Berlin
- Thursday, 03.07.2025, 10:15 (WIAS-405-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Charles Miranda, Ecole Centrale de Nantes, Frankreich:
Properties and optimization of compositional tensor networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this work, we introduce compositional tensor networks (CTN), as a new approximation format merging the strengths of low-rank tensor formats and neural networks. Tensor networks have gained prominence in high-dimensional data analysis and functional approximation, particularly for their robustness and computational efficiency. Neural networks, while more powerful, often require extensive resources and time for training.CTNs combine the benefits of both approaches. We also propose a training procedure for this architecture based on the natural gradient descent. The natural gradient is known for being invariant under reparameterization and for aligning with the true functional gradient under an appropriate metric. This frequently leads to faster and more stable convergence compared to standard Euclidean-gradient-based optimization. Although computing the natural gradient is generally intractable in high-dimensional settings, we show that in the CTN context, it can be computed efficiently using tensor algebra. Moreover, the structure of CTNs allows the use of low-rank constraints during training, further improving computational scalability. The efficiency of this approach is illustrated on benchmark problems in regression.
Host
WIAS Berlin - Wednesday, 09.07.2025, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Johannes Bäumler, UCLA:
tba
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
tba
Host
WIAS Berlin
- Wednesday, 09.07.2025, 14:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Amru Hussein, Universität Kassel:
The three limits of the hydrostatic approximation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The primitive equations are a large scale model for ocean and atmosphere. Formally, they are derived from the 3D-Navier--Stokes equations by the assumption of a hydrostatic balance. This can be formalized by a rescaling procedure on an $varepsilon$-thin domain where one considers anisotropic viscosities with vertical viscosity $varepsilon^gamma$ and $varepsilon$-independent horizontal viscosity. Now, the choice of the order $gamma$ leads to different limit equations:
For $gamma=2$, one obtains the primitive equations with full viscosity term $-Delta$;
For $gamma>2$, one obtains the primitive equations with only horizontal viscosity term $- Delta_H$;
For $gamma <2$, one obtains the 2D Navier-Stokes equations.
Thus, there are three possible limits of the hydrostatic approximation depending on the assumption on the vertical viscosity. Here, we show how maximal regularity methods and quadratic inequalities - reminiscent of the Fujita-Kato methods - can be an efficient approach to prove norm-convergences in all three cases. This is a joint work with Ken Furukawa, Yoshikazu Giga, Matthias Hieber, Takahito Kashiwabara, and Marc Wrona, see https://arxiv.org/abs/2312.03418 for a preprint.
Further Informations
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 09.07.2025, 15:30 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
A mediocre two-component variant of the famous result on equilibration in scalar Fokker--Planck equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
One of the most striking by-now-classical results on Wasserstein gradient flows is the one about exponential equilibration in nonlinear Fokker--Planck equations: if the nonlinearity satisfies McCann's condition, and the potential is lambda-uniformly convex, then any solution tends to the steady state at exponential rate lambda. The proof a la Felix Otto is a remarkable application of uniform displacement convexity. Despite lots of efforts and some progress (particularly by people at WIAS), no result of comparable generality and simplicity has ever been derived for a system of two such Fokker--Planck equations that are coupled by means of cross diffusion. In this talk, we indicate the main difficulty, which is the total break-down of the displacement convexity as soon as coupling is introduced, no matter how tame. Our main result is that for sufficiently weak coupling, equilibration still happens exponentially fast, with a rate lambda, reduced by the coupling strength. The proof is based on the lambda-uniform displacement convexity of the decoupled system, and treats the non-convexity as deformation, using non-standard nonlinear functional inequalities. A central challenge is that the steady state is non-explicit and compactly supported. Some adaptations of the idea are discussed as well: to systems of non-local aggregation equations, to a Keller--Segel system from chemotaxis, and to the second-order destabilized fourth order thin film equation. This is joint work with Lisa Beck (Augsburg), Christian Parsch (TUM), and Martina Zizza (SISSA).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 15.07.2025, 10:15 (WIAS-405-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. André Massing, Norwegian University of Science and Technology, Norwegen:
Cut finite element methods for complex multi-physics problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Many advanced computational problems in engineering and biology require the numerical solution of multidomain, multidimension, multiphysics and multimaterial problems with interfaces. When the interface geometry is highly complex or evolving in time, the generation of conforming meshes may become prohibitively expensive, thereby severely limiting the scope of conventional discretization methods.In this talk we focus on the so-called cut finite element methods (CutFEM) as one possible remedy. The main idea is to design a discretization method which allows for the embedding of purely surface-based geometry representations into structured and easy-to-generate background meshes. In the first part of the talk, using the Cahn-Hilliard and biharmonic equation as starting points, we explain how the CutFEM framework leads to accurate and optimal convergent discretization schemes for a variety of PDEs posed on complex geometries. Afterwards we show that the CutFEM framework can also be used to discretize surface-bound PDEs as well as mixed-dimensional problems where PDEs are posed on domains of different topological dimensionality. In the second part of the talk, we discuss how the CutFEM approach can be employed when discretizing PDEs on evolving domains, and showcase the methodology by considering fluid flow problem involving moving interfaces including Navier-Stokes on moving domains and two-phase flow problem. We conclude with a short outlook of current activities focusing on complex interface problems.
Host
WIAS Berlin - Monday, 21.07.2025, 14:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Prof. Osinga Hinke M, The University of Auckland, Neuseeland:
Phase resetting in a system of coupled Van der Pol oscillators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Coupled nonlinear oscillators are found in many application contexts; specific examples in photonics are coupled optical cavities and ring resonators. Synchronisation properties of such systems can be probed by studying the response to external perturbations: after relaxation back to the stable oscillation, there is generally a phase shift. Important information can be gained by studying such phase resets as a function of when the perturbation is applied during the oscillation. We present a case study of a prototypical example: two coupled 1:1 phase-locked Van der Pol oscillators. In contrast to single oscillators, this system has a phase space of dimension four. In particular, the basin of attraction of the stable synchronised oscillation has a complicated boundary, and we show how this affects the observed phase resetting in unexpected ways.
Further Informations
Forschungsseminar Mathematische Modelle der Photonik
Host
WIAS Berlin
- September 29 – October 1, 2025 (WIAS-ESH)
- Workshop/Konferenz: Mathematical Analysis of Fluid Flows by Variational Methods
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Freie Universität Berlin
Universität Leipzig
WIAS Berlin
- October 15 – 17, 2025 (WIAS-ESH)
- Workshop/Konferenz: Recent Developments in Spatial Interacting Random Systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- November 3 – 7, 2025 (WIAS-Library)
- Workshop/Konferenz:
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstract
The ARISE project (Analysis of Robust Numerical Solvers for Innovative Semiconductors in View of Energy Transition) brings together the RAPSODI team at Inria Lille and the NUMSEMIC team at WIAS Berlin. It focuses on developing advanced mathematical and numerical models for drift-diffusion models for charge transport with mobile ions, with applications for novel semiconductor devices such as perovskite solar cells and memristors, as well as ionic solutions or corrosion phenomena.
Host
WIAS Berlin