Veranstaltungen

Mittwoch, 04.06.2025, 10:00 Uhr (WIAS-HVP-3.13)

Forschungsseminar Mathematische Statistik
Dr. Sebastian Kassing, TU Berlin:
Stochastic optimization: From quadratic programs to the training of neural networks
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
Many foundational results in (stochastic) optimization-ranging from convergence guarantees and rates to asymptotic normality-have been derived under strong convexity assumptions or even for quadratic objective functions. However, such assumptions often fail to hold in modern machine learning applicati- ons, where objectives are typically non-convex. This talk explores a recent line of research that extends classical results in stochastic gradient-based optimization to broader classes of functions satisfying the Polyak-Lojasiewicz (PL) inequality, a condition that is signficantly more relevant for practical deep lear- ning models. We consider typical acceleration techniques such as Polyak's Heavy Ball and Ruppert-Polyak averaging and use a geometric interpretation of the PL-inequality to show that many algorithmic properties extend to a more general and realistic class of objectives

Weitere Informationen
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

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin

Mittwoch, 04.06.2025, 11:30 Uhr (WIAS-405-406)

Seminar Interacting Random Systems
Elena Pulvirenti, Delft University of Technology:
Metastability for the Curie--Weiss--Potts model with unbounded random interactions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
I will first introduce the model, i.e. a disordered version of the mean-field q-spin Potts model, where the interaction coefficients between spins are general independent random variables. These random variables are chosen to have fixed mean (for simplicity taken to be 1), well defined log-moment generating function and finite variance. I will then present quantitative estimates of metastability in the regime of large number of particles at fixed temperature, when the system evolves according to a Glauber dynamics. This means that the spin configuration is viewed as a Markov chain where spins flip according to Metropolis rates at a fixed inverse temperature. Our main result identifies conditions ensuring that, with high probability, the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. Our proofs use the potential-theoretic approach to metastability in combination with concentration inequalities. Based on a joint work in collaboration with Johan Dubbeldam, Vicente Lenz and Martin Slowik.

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin

Mittwoch, 04.06.2025, 14:15 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Junprof. Dr. Theresa Simon, Universität Münster:
Higher degree minimizers in the magnetic skyrmion problem
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
In extremely thin ferromagnetic films, an additional interaction, the so-called Dzyaloshinskii-Moriya interaction (DMI), arises in the micromagnetic energy. In such materials, topologically nontrivial, point-like configurations of the magnetization called magnetic skyrmions are observed, which are of great interest in the physics community due to possible applications in high-density data storage. We will discuss the problem of characterizing skyrmions in the setting of bounded domains with Dirichlet data. For single skyrmions, we resolve this question by describing them in the regime of dominating exchange (or Dirichlet) energy. As in this limit skyrmions collapse into a point, we rely on a quantitative rigidity result for degree 1 harmonic maps into the two-dimensional sphere. Turning to the much harder problem of multiple skyrmions, we demonstrate existence of higher degree minimizers.

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Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Donnerstag, 05.06.2025, 14:00 Uhr (WIAS-405-406)

Seminar Numerische Mathematik
Adrian Hill, TU Berlin:
Composable sparse automatic differentiation in Julia
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
While Automatic Differentiation (AD) is widely used in scientific computing and machine learning, Automatic Sparse Differentiation (ASD) remains an underutilized technique?despite its performance potential. We provide an overview of core ASD concepts, notably sparsity pattern detection and coloring. To make ASD more accessible for practitioners, we introduce a novel open-source pipeline that brings ASD capabilities to all major Julia AD backends. This pipeline includes DifferentiationInterface.jl, a unified interface for over a dozen AD libraries, and SparseConnectivityTracer.jl (SCT), a performant implementation of Jacobian and Hessian sparsity detection via operator overloading. SCT computes both local and global sparsity patterns, naturally avoids dead-ends in compute graphs, and requires no code modifications. Notably, our ASD pipeline often outperforms standard AD for one-off computations, previously thought impractical in Julia due to slower sparsity detection methods.

Veranstalter
WIAS Berlin

Mittwoch, 11.06.2025, 10:00 Uhr (WIAS-HVP-3.13)

Forschungsseminar Mathematische Statistik
Dr. Dimitri Konen, University of Cambridge, GB:
Data assimilation with the 2D Navier-Stokes equations: Optimal Gaussian asymptotics for the posterior measure
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
A functional Bernstein von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier-Stokes equation where a Gaussian process prior is assigned to the initial condition of the system. The posterior measure, which provides the update in the space of all trajectories arising from a discrete sample of the dynamics, is shown to be approximated by a Gaussian random function arising from the solution to a linear parabolic PDE with Gaussian initial condition. The approximation holds in the strong sense of the supremum norm on the regression functions, showing that predicting future states of Navier-Stokes systems admits root(N)-consistent estimators even for commonly used nonparametric models. Consequences to credible bands and uncertainty quantification are discussed, and a functional minimax theorem is derived that describes the Cramer-Rao lower bound for estimating the state of the non-linear system, which is attained by the data assimilation algorithm.

Weitere Informationen
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

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
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

Mittwoch, 11.06.2025, 14:15 Uhr (WIAS-ESH)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Martin Brokate, WIAS & Technische Universität München:
Derivatives of rate-independent evolutions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In rate-independent evolutions, the solution depends on the forcing in a rate-independent manner, that is, if we transform the forcing w.r.t. time, the corresponding solution transforms in the same way. We discuss the question whether this operator (forcing to solution), which is not smooth, nevertheless possesses derivatives of some kind. We show that in a certain basic situation - equivalently described by an evolution variational inequality, a sweeping process or an energetic system - the directional derivative exists and is characterized by a variational system.

Veranstalter
Humboldt-Universität zu Berlin
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

Dienstag, 17.06.2025, 13:30 Uhr (WIAS-405-406)

Seminar Numerische Mathematik
Prof. Dr. Raimund Bürger, Universidad de Concepción, Chile:
Numerical solution of multispecies kinematic flow models through invariant-region-preserving WENO schemes
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
Multispecies kinematic flow models are defined by systems of N strongly coupled, nonlinear first-order conservation laws, where the solution is a vector of N partial volume fractions or densities. The solution vector should take values in a set of physically relevant values (i.e., the components are nonnegative and sum up at most to a given maximum value). In the 1D case, it is shown that this set, the so-called invariant region, is preserved by numerical solutions produced by a new family of high-order finite volume numerical schemes adapted to this class of models [J. Barajas-Calonge, R. Bürger, P. Mulet and L.M. Villada, Invariant-region-preserving WENO schemes for one-dimensional multispecies kinematic flow models, J. Comput. Phys. 537 (2025), article 114081]. To achieve this property, and motivated by [X. Zhang, C.-W. Shu, On maximum-principle-satisfying high order schemes for scalar conserva- tion laws, J. Comput. Phys. 229 (2010) 3091-3120], a pair of linear scaling limiters is applied to a high-order weighted essentially non-oscillatory (CWENO) polynomial reconstruction [D. Levy, G. Puppo G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, ESAIM: Math. Model. Numer. Anal. 33 (1999) 547-571] to obtain invariant-region-preserving (IRP) high-order polynomial reconstructions. These reconstructions are combined with a first-order numerical flux to obtain a high-order numerical scheme for the system of conservation laws. It is proved that this scheme satisfies an IRP property under a suitable CFL condition. For the 2D case, we study a polydisperse sedimentation model consisting in a system of conservation laws coupled with a Stokes problem describing the velocity of the mixture. We propose a second-order IRP WENO scheme for the numerical approximation. The theoretical analysis is corroborated with numerical simulations in some scenarios of interest. This presentation is based on joint work with Juan Barajas-Calonge and Luis Miguel Villada (Universidad del Bío-Bío, Concepción, Chile) and Pep Mulet (Universitat de València, Spain)

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