Veranstaltungen
- Mittwoch, 14.05.2025, 10:00 Uhr (WIAS-HVP-3.13)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Estimation and inference for deep neuronal networks and inverse problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstrakt
The talk discusses two important issues in modern high-dimensional statistics. Success of DNN in practical applications is at the same time a great challenge for statistical theory due to the "curse of dimensionality” problem. Manifold type assumptions are not really helpful and do not explain the double descent phenomenon when the DNN accuracy improves with of overparametrization. We offer a different view on the problem based on the notion of effective dimension and a calming device. The idea is to decouple the structural DNN relation by extending the parameter space and use a proper regularization without any substantial increase of the effective dimension.The other related issue is the choice of regulation in inverse problems. We show that a simple ridge penalty (Tikhonov regularization) does a good job in any inverse problem for which the operator is more regular than the unknown signal. In the opposite case, one should use a model reduction technique like spectral cut-off. Estimation and inference for Deep Neuronal Networks and inverse problems.
Weitere Informationen
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
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Mittwoch, 14.05.2025, 14:00 Uhr (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
Solvability and optimal control in spatially structured epidemic models
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Compartmental models are widely used in the mathematical modeling of infectious diseases, where the population is divided into distinct groups or compartments based on disease status. In this talk, we present results - obtained in collaboration with various co-authors - related to compartmental epidemic models that evolve within spatially heterogeneous environments. These models lead to nonlinear systems of reaction-diffusion partial differential equations, subject to homogeneous Neumann boundary conditions and appropriate initial conditions. Particular attention is given to a class of models incorporating a modified chemotaxis-type term, reflecting movement influenced by spatial infection gradients. We will discuss existence and uniqueness of solutions, and outline some optimal control problems.
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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Mittwoch, 14.05.2025, 15:30 Uhr (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Andrea Signori, Politecnico di Milano, Italien:
Mathematical models of active phase separation and droplet dynamics
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Active phase separation gives rise to striking phenomena, such as the suppression of coarsening and the spontaneous growth and division of droplets, that sharply contrast with the behavior seen in classical systems. Whereas classical phase separation favors the growth of larger domains at the expense of smaller ones, chemically active mixtures can sustain a stable population of droplets with finite size. These dynamics have been proposed as a model for protocells, shedding light on the emergence of self-organized prebiotic structures and the transition from non-living to living matter. In this talk, I will present a mathematical framework for modeling the dynamics of active droplets, using both the phase-field formulation (via the Cahn--Hilliard equation) and the sharp-interface limit (described by the Mullins--Sekerka free-boundary problem). I will explore the connection between these two approaches and discuss the well-posedness and stability of the resulting models, focusing on planar and radial configurations. Finally, I will present numerical simulations that support the asymptotic analysis and highlight complex behaviors such as droplet division and shell formation.
Weitere Informationen
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Donnerstag, 15.05.2025, 14:00 Uhr (WIAS-405-406)
- Seminar Numerische Mathematik
Dr. Peter Munch, Technische Universität Berlin:
The deal.II finite-element library: recent developments and applications
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
deal.II is an open-source general-purpose finite-element C++ library with origins at the University of Heidelberg in 1997. Since then, it has evolved into a mature and worldwide developed and used mathematical software library (including at WIAS and TU Berlin). It is the basis of applications ranging from traditional application fields like computational solid mechanics, fluid mechanics, biomechanics, and geosciences to more ?exotic? fields of research such as quantum and plasma physics. The scalability of deal.II has been shown by solving partial differential equations with trillions of unknowns on 300k processes. For its outstanding contributions to the development and use of mathematical and computational tools and methods for the solution of science and engineering problems, deal.II was awarded the prestigious ?SIAM/ACM Prize in Computational Science and Engineering 2025?. In this talk, we will give a short introduction into deal.II, discuss recent developments in the library and present new use cases.
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Seminar Numerische Mathematik
Veranstalter
WIAS Berlin
- Montag, 19.05.2025, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Peter Gracar, University of Leeds:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Weitere Informationen
Seminar Interacting Random Systems
Veranstalter
WIAS Berlin
- Dienstag, 20.05.2025, 14:00 Uhr (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Max Fröhlich, WIAS Berlin:
Quantum circuit simulation with a localized dynamic time-dependent variational principle
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We introduce a novel tensor network simulation method for quantum circuits that addresses key limitations inherent in the widely used time-evolving block decimation algorithm (TEBD). TEBD suffers from truncation errors during many-body dynamics and, more critically, faces challenges in simulating long-range gates?requiring additional SWAP gate decompositions that further induce truncation errors and computational overhead. By representing quantum states in the matrix product state (MPS) format and evolving them via a locally adaptive time-dependent variational principle (TDVP), our approach rigorously projects the generator of each quantum gate onto the tangent space of the MPS manifold. This allows for dynamic adjustment of bond dimensions, accurately capturing entanglement growth while efficiently simulating long-range gates directly, without resorting to SWAP gates. Benchmarking against conventional TEBD simulations demonstrates that our local TDVP simulation scheme achieves improved numerical stability, lower bond dimensions with at least the fidelity of TEBD, paving the way for more reliable large-scale quantum circuit simulations.
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Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Veranstalter
WIAS Berlin
- Mittwoch, 21.05.2025, 10:00 Uhr (WIAS-HVP-3.13)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Yi Yu, University of Warwick, GB:
Contextual dynamic pricing: Algorithms, optimality and local differential privacy constraints
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstrakt
We study contextual dynamic pricing problems where a firm sells products to $T$ sequentially-arriving consumers, behaving according to an unknown demand model. The firm aims to minimize its regret over a clairvoyant that knows the model in advance. The demand follows a generalized linear model (GLM), allowing for stochastic feature vectors in $mathbb R^d$ encoding product and consumer information. We first show the optimal regret is of order $sqrtdT$, up to logarithmic factors, improving existing upper bounds by a $sqrtd$ factor. This optimal rate is materialized by two algorithms: an explore-then-commit (ETC) algorithm and a confidence bound-type algorithm. A key insight is an intrinsic connection between dynamic pricing and contextual multi-armed bandit problems with many arms with a careful discretization. We further extend our study to adversarial contexts and propose algorithms that are statistically and computationally more efficient than existing methods in the literature. We further study contextual dynamic pricing under local differential privacy (LDP) constraints. We propose a stochastic gradient descent-based ETC algorithm achieving regret upper bounds of order $dsqrtT/epsilon$, up to logarithmic factors, where $epsilon>0$ is the privacy parameter. The upper bounds with and without LDP constraints are matched by newly constructed minimax lower bounds, characterizing costs of privacy. Moreover, we extend our study to dynamic pricing under mixed privacy constraints, improving the privacy-utility tradeoff by leveraging public data. This is the first time such setting is studied in the dynamic pricing literature and our theoretical results seamlessly bridge dynamic pricing with and without LDP. Extensive numerical experiments and real data applications are conducted to illustrate the efficiency and practical value of our algorithms.
Weitere Informationen
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
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Mittwoch, 21.05.2025, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Adrian Röllin, National University of Singapore:
Centered Subgraph Counts in Dense Random Graphs
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Complex networks appear in many fields, from social media to biology, and understanding their structure often boils down to studying how frequently small subgraphs (such as triangles or squares) appear. In this talk, I will introduce the idea of centered subgraph counts: a way of measuring subgraph occurrences that corrects for the dependence that we observe among regular subgraph counts. By focusing on these centered counts, we can describe and quantify the natural 'fluctuations' in dense random networks via tools first developed by Janson and Nowicki in the study of generalised U-statistics in the 90s. I will explain how these theoretical results lead to practical methods for assessing how well a given network fits a chosen statistical model--often referred to as a goodness-of-fit analysis.
Weitere Informationen
Seminar Interactin Random Systems
Veranstalter
WIAS Berlin
- Mittwoch, 21.05.2025, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Olaf Klein, WIAS Berlin:
Uncertainty quantification for a model for a magnetostrictive material involving a hysteresis operator
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin
Freie Universität Berlin
- Donnerstag, 22.05.2025, 10:00 Uhr (WIAS-ESH)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Michael Hinze, Universität Koblenz:
Shape optimization with Lipschitz methods (joint work with Klaus Deckelnick (Magdeburg) and Philip Herbert (Sussex))
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We present a general shape optimisation framework based on the method of mappings in the Lipschitz topology. We propose and numerically analyse steepest descent and Newton-like minimisation algorithms for the numerical solution of the respective shape optimisation problems. To illustrate our approach we present a selection of PDE constrained shape optimisation problems and compare our findings to results from so far classical Hilbert space methods and recent p-approximations.
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Berlin Oberseminar: Optimization, Control and Inverse Problems
Veranstalter
WIAS Berlin
- Donnerstag, 22.05.2025, 14:00 Uhr (WIAS-ESH)
- Halbleiterseminar
Prof. Band Ram, Mathematics Department, Technion Israel Institute of Technology:
Universality of the band-gap density - From periodic graphs to laminates
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
The spectrum of periodic objects has a band-gap structure. We show that such a spectrum can be described in terms of a linear flow on a torus. This characterization is valid for various periodic structures, from quantum graphs to wave propagation in elastic laminates. Using this approach allows us to prove universal properties of the band-gap density and obtain many useful spectral characteristics.
Veranstalter
WIAS Berlin
- Donnerstag, 22.05.2025, 15:30 Uhr (WIAS-405-406)
- Seminar Numerische Mathematik
Dr. Holger Stephan:
Improvement of the diffusion equation using hyperbolic systems and memory equations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
The diffusion equation is the simplest equation to describe the motion of a particle in a random medium. It is the 0th moment (mass balance) of the more exact kinetic equation (Kramers equation). Higher momentum approximations such as the 1st momentum (momentum balance) and the 2nd momentum (energy balance) are also common. Moment approximations must be closed. We calculate the optimal approximations for various higher moment systems for the case of no external potential. This leads to hyperbolic systems which, as is well known, are difficult to solve numerically. However, systems of diffusion equations with memory terms can be derived from them without loss of information. These can also be converted into common systems of diffusion equations also without loss of information using a recently developed method, which can be solved numerically very well. The result is a much more precise description of the diffusion process.
Veranstalter
WIAS Berlin
- Dienstag, 27.05.2025, 15:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Prof. Dmitry Turaev, Imperial College London, GB:
TBA
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Weitere Informationen
Forschungsseminar Mathematische Modelle der Photonik
Veranstalter
WIAS Berlin
- Mittwoch, 04.06.2025, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Elena Pulvirenti, Delft University of Technology:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Weitere Informationen
Seminar Interacting Random Systems
Veranstalter
WIAS Berlin
- Donnerstag, 05.06.2025, 14:00 Uhr (WIAS-405-406)
- Seminar Numerische Mathematik
Adrian Hill, TU Berlin:
SparseConnectivityTracer.jl
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Veranstalter
WIAS Berlin
- Mittwoch, 11.06.2025, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Michiel Renger, Technische Universität München:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Weitere Informationen
Seminar Interacting Random Systems
Veranstalter
WIAS Berlin
- 16. – 18. Juni 2025 (WIAS-ESH)
- Workshop/Konferenz: Nonlinear Dynamics in Semiconductor Lasers 2025
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
WIAS Berlin
- 23. – 26. Juni 2025 (Harnack-Haus)
- Workshop/Konferenz: 4th Annual Conference of SPP 2265 Random Geometric Systems 2025
mehr ... Veranstaltungsort
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Veranstalter
WIAS Berlin
- Mittwoch, 09.07.2025, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Amru Hussein, Universität Kassel:
The three limits of the hydrostatic approximation
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
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.
Weitere Informationen
Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- 29. September – 1. Oktober 2025 (WIAS-ESH)
- Workshop/Konferenz: Mathematical Analysis of Fluid Flows by Variational Methods
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
Freie Universität Berlin
Universität Leipzig
WIAS Berlin
- 15. – 17. Oktober 2025 (WIAS-ESH)
- Workshop/Konferenz: Recent Developments in Spatial Interacting Random Systems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
WIAS Berlin
- 3. – 7. November 2025 (WIAS-Library)
- Workshop/Konferenz:
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstrakt
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.
Veranstalter
WIAS Berlin