Veranstaltungen
- Donnerstag, 16.05.2024, 14:00 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Medine Demir:
Pressure-robust approximation of the incompressible Navier--Stokes equations in a rotating frame of reference
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
A pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples support the theoretical results.
Veranstalter
WIAS Berlin
- Mittwoch, 15.05.2024, 16:15 Uhr (WIAS-ESH)
- Berliner Kolloquium Wahrscheinlichkeitstheorie
Adrián González-Casanova, UNAM, Mexico and University of California, Berkeley:
Sample Duality
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
Heuristically, two processes are dual if one can find a function to study one process by using the other. Sampling duality is a duality which uses a duality function S(n, x) of the form "what is the probability that all the members of a sample of size n are of a certain type, given that the number (or frequency) of that type of individuals is x". Implicitly, this technique can be traced back to the work of Blaise Pascal. Explic- itly, it was studied in a paper of Martin Möhle in 1999 in the context of population genetics. We will discuss examples for which this technique proves to be useful, including applications to the Simple Exclusion Process and (work in progress) a universality result for the FKPP equation.
Veranstalter
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
- Mittwoch, 15.05.2024, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Erica Ipocoana, Freie Universität Berlin:
Non-isothermal phase-field models for tumor growth
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We present two different diffuse interface models for tumor growth. In this context, the tumor is seen as an expanding mass surrounded by healthy tissues, while the interface in between contains a mixture of both healthy and tumor cells. The evolution of the system is assumed to be governed by biological mechanisms such as proliferation of cells via nutrient consumption and apoptosis. Besides, both the models include the effects of temperature variations. From the medical point of view, it is clear that the temperature does have effects on tumor growth and that in particular hyperthermia can lead to partial or complete destruction of tumor cells. The first model is a Cahn--Hilliard model, while the second is of Allen--Cahn type. After deriving the models following the microforces approach, we focus on proving the well-posedness and compare which regularity we are able to get for the solutions. Part of these results have been obtained in a recent collaboration with Stefania Gatti and Alain Miranville.
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Mittwoch, 15.05.2024, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Adrián Gonzalez Casanova, UNAM, Mexico and University of California, Berkeley:
A random model of Poissonian interacting trajectories inspired by the Lenski experiment
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Random geometric phenomena emerge as a result of mutations and selection within the Lenski experiment. In this presentation, I will delve into A Random Model of Poissonian Interacting Trajectories, which can be derived as a scaling limit from classic models in population genetics. This model exhibits a complex geometric framework, offering insights into the effect of clonal interference on evolutionary dynamics.
Weitere Informationen
Seminar Interacting Random Systems (Online Event)
Veranstalter
WIAS Berlin
- Mittwoch, 15.05.2024, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Fabian Telschow, Humboldt-Universität zu Berlin:
Estimation of the expected Euler characteristic of excursion sets of random fields and applications to simultaneous confidence bands
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
The expected Euler characteristic (EEC) of excursion sets of a smooth Gaussian-related random field over a compact manifold can be used to approximate the distribution of its supremum for high thresholds. Viewed as a function of the excursion threshold, the EEC of a Gaussian-related field is expressed by the Gaussian kinematic formula (GKF) as a finite sum of known functions multiplied by the Lipschitz-Killing curvatures (LKCs) of the generating Gaussian field. In the first part of this talk we present consistent estimators of the LKCs as linear projections of “pinned" Euler characteristic (EC) curves obtained from realizations of zero-mean, unit variance Gaussian processes. As observed data seldom is Gaussian, we generalize these LKC estimators by an unusual use of the Gaussian multiplier bootstrap to obtain consistent estimates of the LKCs of Gaussian limiting fields of non-stationary statistics. In the second part, we explain applications of LKC estimation and the GKF to simultaneous familywise error rate inference, for example, by constructing simultaneous confidence bands and CoPE sets for spatial functional data over complex domains such as fMRI and climate data and discuss their benefits and drawbacks compared to other methodologies.
Weitere Informationen
Der Vortrag findet auch via Zoom statt: https://hu-berlin.zoom-x.de/j/69268586742?pwd=bDZJQTk5TGdnUkVCUk9RWGdsWC9vdz09 Meeting-ID: 692 6858 6742, Passwort: 021844
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Dienstag, 14.05.2024, 15:30 Uhr (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Thomas Möllenhoff, RIKEN Center for Advanced Intelligence Project, Japan:
Variational learning for large deep networks
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
We present extensive evidence against the common belief that variational Bayesian learning is ineffective for large neural networks. First, we show that a popular deep learning method called sharpness-aware minimization (SAM) solves an optimal relaxation of the variational Bayesian objective. Then, we demonstrate that a direct optimization of the variational objective with an Improved Variational Online Newton method (IVON) can consistently match or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of variational learning where we improve fine-tuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence in support of effectiveness of variational methods for deep learning.
Weitere Informationen
Hybrid event. Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Dienstag, 14.05.2024, 14:00 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Marwa Zainelabdeen:
Physics-informed neural networks for convection-dominated convection-diffusion problems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
In the convection-dominated regime, solutions of convection-diffusion problems usually possess layers, which are regions where the solution has a steep gradient. It is well known that many classical numerical discretization techniques face difficulties when approximating the solution to these problems. In recent years, physics-informed neural networks (PINNs) for approximating the solution to (initial-)boundary value problems received a lot of interest. PINNs are trained to minimize several residuals (loss functionals) of the problem in collocation points. In this talk, we introduce various loss functionals for PINNs that are especially designed for convection-dominated convection-diffusion problems. They are numerically tested and compared on two benchmark problems whose solutions possess different types of layers. We observed that certain special functionals reduce the L^2 (?) error compared to the standard residual loss functional. Furthermore, three types of collocation points applied to hardconstrained PINNs are compared: layer-adapted, equispaced and uniformly randomly chosen points. We observe that layer-adapted points work the best for a problem with an interior layer and the worst for a problem with boundary layers.
Veranstalter
WIAS Berlin
- Dienstag, 14.05.2024, 13:30 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Cristian Cárcamo:
Equal-order finite element methods for coupled and multiphysics problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We discuss the well-posedness and error analysis of the Coupled Navier--Stokes--Darcy equations and Biot's Poroelastic equations in this talk. To demonstrate the solvability of the poroelastic continuous issue, we first use the well-known Fredholm Alternative. In order to improve computational efficiency and address the issues raised by the discrete inf-sup condition, we present a novel and stable stabilized numerical system that is tuned for equal polynomial order. Analogous aspects of the Coupled Navier-Stokes Equations are examined. We also perform a numerical analysis to determine the stability of solutions and offer an a priori analysis of them. Lastly, we provide a few numerical illustrations. These examples offer strong proof of the usefulness and effectiveness of the suggested numerical framework.
Veranstalter
WIAS Berlin