Veranstaltungen
- Dienstag, 26.11.2024, 14:00 Uhr (WIAS-Library)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Denis Korolev, WIAS Berlin:
Hybrid physics--informed neural network based dual--scale solver and its applications to learning--informed upscaling
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstrakt
Inspired by the Liquid Composite Molding process for fiber-reinforced composites and its associated multiscale fluid flow structure, we present a novel framework for optimizing physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs), with applications to dual-scale PDE systems. Our hybrid approach approximates the fine-scale PDE using PINNs, producing a PDE residual-based objective subject to a coarse-scale PDE model parameterized by the fine-scale solution. Techniques from materials science introduce feedback mechanisms that yield scale-bridging coupling, resulting in a non-standard PDE-constrained optimization problem. From a discrete standpoint, the formulation represents a hybrid numerical solver that integrates both neural networks and finite elements. In this talk, we present the application setting, mathematical model, and highlights of its analysis, as well as outline perspectives on developing optimization algorithms for the hybrid framework in the infinite-dimensional setting.
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Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Veranstalter
WIAS Berlin
- Mittwoch, 27.11.2024, 10:00 Uhr (WIAS-HVP-3.13)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Julien Chhor, Toulouse School of Economics, Frankreich:
Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts
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Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstrakt
We consider testing the goodness-of-fit of a distribution against alternatives separated in sup norm. We study the twin settings of Poisson-generated count data with a large number of categories and highdimensional multinomials. In previous studies of different separation metrics, it has been found that the local minimax separation rate exhibits substantial heterogeneity and is a complicated function of the null distribution; the rate-optimal test requires careful tailoring to the null. In the setting of sup norm, this remains the case and we establish that the local minimax separation rate is determined by the finer decay behavior of the category rates. The upper bound is obtained by a test involving the sample maximum, and the lower bound argument involves reducing the original heteroskedastic null to an auxiliary homoskedastic null determined by the decay of the rates. Further, in a particular asymptotic setup, the sharp constants are identified. This is a joint work with Subhodh Kotekal and Chao Gao.
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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
- Donnerstag, 28.11.2024, 14:00 Uhr (WIAS-HVP-3.13)
- Seminar Numerische Mathematik
Dr. Lucas Omar Muller, University of Trento, Italien:
Towards real-life computional haemodynamics
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Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstrakt
Understanding the fundamental forces driving human physiology relies on a deep understanding of the circulation. During our daily life, the cardiovascular system is exposed to a wide range of biomechanical environments. This complexity requires a systemic approach to integrate phenomena across various temporal and spatial scales. Most of the research efforts in this do- main have focused on simplified cardiovascular scenarios such as the resting state, the supine position, and occasionally disease conditions. However, the cardiovascular system experiences large deviations from such prototypical conditions, which are, in many cases, highly beneficial to sustaining a healthy life. The impact of fundamental factors such as respiration, control mech- anisms, gravity, diverse physiological states (e.g., exercise or sleep conditions), and the integration of organ-specific physiology and disease into blood flow models has only been partially addressed. This talk aims to explore ongoing work in the field of computational hemodynamics at the systemic scale exploiting an anatomically detailed arterio-venous network 1D model [1] and highlighting modelling and numerical challenges related to simulations that intend to incorporate three aspects that are inextri- cably coupled to the circulation in our routine life: (i) the effect of respiration, (ii) the effect of orthostatic stress, and (iii) the presence of massive microvascular networks.
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Numerics Seminar
Veranstalter
WIAS Berlin
- Dienstag, 03.12.2024, 10:15 Uhr (WIAS-405-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Pedro Perez-Aros, Universidad de Chile:
The boosted double-proximal subgradient algorithm for nonconvex optimization
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
This presentation introduces the Boosted Double-Proximal Subgradient Algorithm (BDSA), a novel splitting method for tackling general structured nonsmooth and nonconvex optimization problems expressed as sums and differences of composite functions. BDSA combines subgradients derived from data and proximal steps, augmented by a linesearch strategy to boost performance. We establish the convergence of BDSA under the Kurdyka-Łojasiewicz property and analyze its convergence rate. The talk concludes with numerical experiments illustrating the algorithm's effectiveness and robustness across various test scenarios.
Veranstalter
WIAS Berlin
- Dienstag, 03.12.2024, 15:00 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Nikita Doikov, École Polytechnique Fédérale de Lausanne, Schweiz:
Stochastic second-order optimization with momentum
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
In this talk, we discuss stochastic second-order algorithms for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that momentum provably improves the variance of stochastic estimates and allows the method to converge for any noise level. Using the cubic regularization technique, we prove a global convergence rate for our method on general non-convex problems to a second-order stationary point, even when using only a single stochastic data sample per iteration. This starkly contrasts with all existing stochastic second-order methods for non-convex problems, which typically require large batches. Joint work with El Mahdi Chayti and Martin Jaggi.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Dienstag, 03.12.2024, 15:45 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Anton Rodomanov, CISPA Helmholtz Center:
Optimizing (L_0, L_1)-smooth functions by gradient methods
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
We study gradient methods for solving an optimization problem with an (L_0, L_1)-smooth objective function. This problem class generalizes that of Lipschitz-smooth problems and has gained interest recently, as it captures a broader range of machine learning applications. We provide novel insights into the properties of this function class and develop a general framework for analyzing optimization methods for (L_0, L_1)-smooth functions in a principled manner. While our convergence rate estimates recover existing results for minimizing the gradient norm for nonconvex problems, our approach allows us to significantly improve the current state-of-the-art complexity results in the case of convex problems. We show that both the gradient method with Polyak stepsizes and the normalized gradient method, without any knowledge of the parameters L_0 and L_1, achieve the same complexity bounds as the method with the knowledge of these constants. In addition to that, we show that a carefully chosen accelerated gradient method can be applied to (L_0, L_1)-smooth functions, further improving previously known results.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Mittwoch, 04.12.2024, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Günter Last, Karlsruher Institut für Technologie:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Veranstalter
WIAS Berlin
- Mittwoch, 04.12.2024, 15:15 Uhr (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Georg Heinze, WIAS Berlin:
Discrete-to-continuum limit for reaction-diffusion systems via variational convergence of gradient systems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
This talk is about a convergence result for the spatial discretization of a reaction-diffusion system. The approximation is based on a homogeneous lattice, where in each node a reaction-ODE system describes the evolution of the concentrations, and where the transport between the different lattice nodes is given by additional exchange reactions. Assuming detailed balance, this large coupled reaction system can be understood as a (generalized) gradient flow characterized by cosh-type dissipation potentials and the relative entropy. Sending the lattice width to zero, we show how the limit reactiondiffusion-PDE system can be recovered with variational methods and an energy-dissipation principle. The talk is based on joint work with Alexander Mielke and Artur Stephan.
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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Mittwoch, 11.12.2024, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Leoni Carla Wirth, Universität Göttingen:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Veranstalter
WIAS Berlin
- Mittwoch, 11.12.2024, 15:15 Uhr (WIAS-405-406)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Sebastian Bechtel, Université Paris-Saclay, Frankreich:
What we know about square roots of elliptic systems - and a bit more!
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
In my talk we consider elliptic systems in divergence form, potentially perturbed by a multiplicative perturbation from the left, with measurable, elliptic coefficients. I will first explain why we should care for non-smooth coefficients and why they are difficult to treat. Afterwards, we will turn our focus to elliptic systems that are defined in rough domains and subject to mixed boundary conditions, I will introduce our geometric framework by virtue of examples and present which positive results we can obtain in this scope, both L2 theory and (the optimal range of) Lp theory. Finally, I will conclude with some open questions (and what we expect to obtain for them).
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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Dienstag, 17.12.2024, 15:00 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexey Kroshnin, WIAS Berlin:
On concentration inequalities for unbounded matrix super-martingales
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Weitere Informationen
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Mittwoch, 15.01.2025, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Xiaorui Zuo, National University of Singapore , Singapur:
Cryptos have rough volatility and correlated jumps
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
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