Upcoming Events

Due to infection prevention measures, participation in events at the institute is presently not possible for guests.

Many events are currently organized online. Information on how to access these events can be found by clicking “more” below the respective entry.


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Tuesday, 02.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yunfei Huang, Ludwig-Maximilians-Universität München:
Advanced data analysis for traction force microscopy and data-driven discovery of physical equations (online talk)
more ... Location
Online Event

Abstract
The plummeting cost of collecting and storing data and the increasingly available computational power in the last decade have led to the emergence of new data analysis approaches in various scientific fields. Frequently, the new statistical methodology is employed for analyzing data involving incomplete or unknown information. In this thesis, new statistical approaches are developed for improving the accuracy of traction force microscopy (TFM) and data-driven discovery of physical equations. TFM is a versatile method for the reconstruction of a spatial image of the traction forces exerted by cells on elastic gel substrates. The traction force field is calculated from a linear mechanical model connecting the measured substrate displacements with the sought-for cell-generated stresses in real or Fourier space, which is an inverse and ill-posed problem. This inverse problem is commonly solved making use of regularization methods. Here, we systematically test the performance of new regularization methods and Bayesian inference for quantifying the parameter uncertainty in TFM. We compare two classical schemes, L1- and L2-regularization with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. We find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.. We further combine the Bayesian L2 regularization with the computational speed of Fast Fourier Transform algorithms to develop a fully automated method for noise reduction and robust, standardized traction-force reconstruction that we call Bayesian Fourier transform traction cytometry (BFTTC). This method is made freely available as a software package with graphical user-interface for intuitive usage. Using synthetic data and experimental data, we show that these Bayesian methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Next, we employ our methodology developed for the solution of inverse problems for automated, data-driven discovery of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). To find the equations governing a measured time-dependent process, we construct dictionaries of non-linear candidate equations. These candidate equations are evaluated using the measured data. With this approach, one can construct a likelihood function for the candidate equations. Optimization yields a linear, inverse problem which is to be solved under a sparsity constraint. We combine Bayesian compressive sensing using Laplace priors with automated thresholding to develop a new approach, namely automatic threshold sparse Bayesian learning (ATSBL). ATSBL is a robust method to identify ODEs, PDEs, and SDEs involving Gaussian noise, which is also referred to as type I noise. We extensively test the method with synthetic datasets describing physical processes. For SDEs, we combine data-driven inference using ATSBL with a novel entropy-based heuristic for discarding data points with high uncertainty. Finally, we develop an automatic iterative sampling optimization technique akin to Umbrella sampling. Therewith, we demonstrate that data-driven inference of SDEs can be substantially improved through feedback during the inference process if the stochastic process under investigation can be manipulated either experimentally or in simulations.

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Wednesday, 03.03.2021, 11:30 (Online Event)
Seminar Interacting Random Systems
Cecile Mailler, The University of Bath, GB:
The ants walk: finding geodesics in graphs using reinforcement learning
more ... Location
Online Event

Abstract
How does a colony of ants find the shortest path between its nest and a source of food without any means of communication other than the pheromones each ant leave behind itself? In this joint work with Daniel Kious (Bath) and Bruno Schapira (Marseille), we introduce a new probabilistic model for this phenomenon. In this model, the nest and the source of food are two marked nodes in a finite graph. Ants perform successive random walks from the nest to the food, and ths distribution of the n-th walk depends on the trajectories of the (n-1) previous walks through some linear reinforcement mechanism. Using stochastic approximation methods, couplings with Pólya urns, and the electric conductances method for random walks on graphs, we prove that, in this model, the ants indeed eventually find the shortest path(s) between their nest and the source food.

Further Informations
Seminar Interacting Random Systems (Online Event)

Host
WIAS Berlin
Tuesday, 09.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Tuesday, 16.03.2021, 13:30 (Online Event)
Seminar Numerische Mathematik
Dr. Jürgen Fuhrmann, WIAS Berlin:
PDELib.jl: Towards software components for the numerical solution of partial differential equations in Julia
more ... Location
Online Event

Abstract
In recent years, in particular since the release of version 1.0, the Julia programming language gained significant momentum in fields related to scientific computing and data science. Taking advantage of accumulated experience and know-how in language design, designed around the just-in-time compilation paradigm, and featuring first class multidimensional array handling, it allows for the implementation of complex numerical algorithms without sacrificing efficiency. In recent years, in particular since the release of version 1..0, the Julia programming language gained significant momentum in fields related to scientific computing and data science.
In the talk, we will give a short overview on features of the Julia language which renders it well suited for the implementation of solvers for complex systems of partial differential equations, including multiple dispatch allowing for the implementation of automatic differentiation, interface oriented API design and its package manager supporting reusability and reproducibility.
We will report on the successful steps towards the implementation of software components for the numerical solution of PDEs.. Focus will be on the package VoronoiFVM.jl and supporting packages.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Tuesday, 16.03.2021, 15:00 (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Kostas Papafitsoros, WIAS Berlin:
Optimization with learning-informed differential equation constraints and its applications (online talk)
more ... Location
Online Event

Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Host
WIAS Berlin
Thursday, 18.03.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Leo Rebholz, Clemson University, USA:
Anderson acceleration and how it speeds up convergence in fixed point iterations
more ... Location
Online Event

Abstract
Anderson acceleration (AA) is an extrapolation technique originally proposed in 1965 that recombines the most recent iterates and update steps in a fixed point iteration to improve the convergence properties of the sequence. Despite being successfully used for many years to improve nonlinear solver behavior on a wide variety of problems, a theory that explains the often-observed accelerated convergence was lacking. In this talk, we give an introduction to AA, then present a proof of AA convergence which shows that it improves the linear convergence rate based on a gain factor of an underlying optimization problem, but also introduces higher order terms in the residual error bound. We then discuss improvements to AA based on our convergence theory, and show numerical results for the algorithms applied to several application problems including Navier--Stokes, Boussinesq, and nonlinear Helmholtz systems.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin
Thursday, 15.04.2021, 14:00 (Online Event)
Seminar Numerische Mathematik
Prof. Julia Novo, Universidad Autónoma de Madrid, Spanien:
Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows
more ... Location
Online Event

Abstract
Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are presented. We consider two cases: the case in which the snapshots are based on a non inf-sup stable method and the case in which the snapshots are based on an inf-sup stable method. For both cases we construct approximations to the velocity and the pressure. For the first case, we analyze a method in which the snapshots are based on a stabilized scheme with equal order polynomials for the velocity and the pressure with local projection stabilization (LPS) for the gradient of the velocity and the pressure. For the POD method we add the same kind of LPS stabilization for the gradient of the velocity and the pressure as the direct method, together with grad-div stabilization. In the second case, the snapshots are based on an inf-sup stable Galerkin method with grad-div stabilization and for the POD model we also apply grad-div stabilization. In this case, since the snapshots are discretely divergence-free, the pressure can be removed from the formulation of the POD approximation to the velocity. To approximate the pressure, needed in many engineering applications, we use a supremizer pressure recovery method. Error bounds with constants independent of inverse powers of the viscosity parameter are proved for both methods. Numerical experiments show the accuracy and performance of the schemes.

Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Host
WIAS Berlin