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Agenda

ical

29 april 2024 15:45 t/m 16:45

[STAT/AP] Botond Szabo: tba

02 mei 2024 16:00 t/m 17:00

[PDE&A] Annika Bach: Discrete-to-continuum variational analysis for Ising and Spin models

This seminar is thought as an introductory talk to discrete-to-continuum variational analysis. Here the general objective is to characterise the macroscopic behaviour of energy-driven atomistic systems while keeping the scale-dependent relevant microscopic information. This is done via Γ-convergence, which allows to coarse-grain discrete functionals to their continuum counterparts as the discretisation parameter vanishes. In this talk we will focus on some models with a particularly rich energy landscape, namely Ising and spin models such as the classical XY-model. In the first part I will give a short introduction to the topic and review some of the classical results in this context. In the second part I will present some recent results obtained in collaboration with Marco Cicalese, Leonard Kreutz, and Gianluca Orlando on the antiferromagnetic XY-model on the triangular lattice.

03 mei 2024 12:30 t/m 13:15

[NA] Jakob Zech: Nonparametric Distribution Learning via Neural ODEs

In this talk, we explore approximation properties and statistical aspects of Neural Ordinary Differential Equations (Neural ODEs). Neural ODEs are a recently established technique in computational statistics and machine learning, that can be used to characterize complex distributions. Specifically, given a fixed set of independent and identically distributed samples from a target distribution, the goal is either to estimate the target density or to generate new samples. We first investigate the regularity properties of the velocity fields used to push forward a reference distribution to the target. This analysis allows us to deduce approximation rates achievable through neural network representations. We then derive a concentration inequality for the maximum likelihood estimator of general ODE-parametrized transport maps. By merging these findings, we are able to determine convergence rates in terms of both the network size and the number of required samples from the target distribution. Our discussion will particularly focus on target distributions within the class of positive \(C^k\) densities on the \(d\)-dimensional unit cube \([0,1]^d\).

07 mei 2024 16:00 t/m 17:00

[AN] Chenxi Deng: TBA

13 mei 2024 15:45 t/m 16:45

[STAT/AP] Sonja Cox: tba

14 mei 2024 16:00 t/m 17:00

[AN] Michal Wrochna: TBA

16 mei 2024 16:00 t/m 17:00

[PDE&A] Paul Zegeling: A generalized midpoint-based BV-method for unstable PDEs (and beyond)

We will discuss a generalized midpoint-based boundary-value method and its application to unstable and ill-posed partial differential equations (PDEs). Furthermore, an extension of this technique to DE systems with periodic
solutions, e.g., the harmonic oscillator and predator-prey equations will be proposed.

Boundary-value methods (BVMs) are generalizations of traditional time-integrators such as linear multistep or Runge-Kutta methods. They make use of additional final and, if appropriate, extra initial conditions as well.

The generalized midpoint-based BMV has the special property that its stability region is the whole complex plane (excluding the imaginary axis). This opens interesting new application areas (compared to the well-known and widely-accepted time-integration techniques): the backward heat equation and similar ill-posed or unstable PDEs. Examples will be given for several models in this class. In addition, replacing the final conditions in the BVM by periodic conditions, we can apply this approach to DEs with periodic solution behaviour. Especially, it is interesting to investigate models with center points, limit cycles and where the conservation of energy in Hamiltonian DE systems plays a role.

21 mei 2024 16:00 t/m 17:00

[AN] Joris van Winden: TBA

27 mei 2024 15:45 t/m 16:45

[STAT/AP] Collin Drent: Condition-Based Production for Stochastically Deteriorating Systems: Optimal Policies and Learning

Production systems used in the manufacturing industry degrade due to production and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This degradation behavior, and hence the system's reliability, is affected by the system's production rate. While producing at a higher rate generates more revenue, the system's reliability may also decrease. Production should thus be controlled dynamically to trade-off reliability and revenue accumulation in between maintenance moments. We study this dynamic trade-off for (i) systems where the relation between production and degradation is known as well as (ii) systems where this relation is not known and needs to be learned on-the-fly from condition data. For systems with a known production-degradation relation, we cast the decision problem as a continuous-time Markov decision process and prove that the optimal policy has intuitive monotonic properties. We also present sufficient conditions for the optimality of bang-bang policies and we characterize the structure of the optimal interval between scheduled maintenance moments. For systems with an a-priori unknown production-degradation relation, we propose a Bayesian procedure to learn the unknown degradation rate under any production policy from real-time condition data. Numerical studies indicate that on average across a wide range of practical settings (i) condition-based production increases profits by 50% compared to static production, (ii) integrating condition-based production and maintenance interval selection increases profits by 21% compared to a state-of-the-art approach, and (iii) our Bayesian approach performs close, especially in the bang-bang regime, to an Oracle policy that knows each system's production-degradation relation.

28 mei 2024 16:00 t/m 17:00

[AN] Hans Maassen: TBA

30 mei 2024 16:00 t/m 17:00

[PDE&A] Viktoria Freingruber

31 mei 2024 12:30 t/m 13:15

[NA] Hyea Hyun Kim: Partitioned neural network approximation to partial differential equations and its training performance enhancement utilizing domain decomposition algorithms

With the success of deep learning technologies in many scientific and engineering applications, neural network approximation methods have emerged as an active research area in numerical partial differential equations. However, the new approximation methods still need further validations on their accuracy, stability, and efficiency so as to be used as alternatives to classical approximation methods. In this talk, we first introduce partitioned neural network approximation to partial differential equations, where neural network functions localized in each small subdomains are employed as a solution surrogate in order to reduce the approximation and optimization errors in the standard single large neural network approximation. The parameters in each local neural network function are then optimized to minimize the corresponding cost function to the model problem. To enhance the parameter training efficiency further, iterative algorithms for the partitioned neural network function can be developed by utilizing classical domain decomposition algorithms and their convergence theory. We finally present promising features in this new approach as a way of enhancing the neural network solution accuracy, stability, and efficiency with some supporting numerical results.

03 juni 2024 15:45 t/m 16:45

[STAT/AP] Eni Musta: tba

04 juni 2024 16:00 t/m 17:00

[AN] Anouk Wisse: TBA

06 juni 2024 16:00 t/m 17:00

[PDE&A] Marco Rehmeier

11 juni 2024 16:00 t/m 17:00

[AN] Rik Westdorp: TBA

13 juni 2024 16:00 t/m 17:00

[PDE&A] María de los Ángeles García Ferrero

17 juni 2024 15:45 t/m 16:45

[STAT/AP] Rui Castro: tba

18 juni 2024 16:00 t/m 17:00

[AN] Palina Salanevich: TBA

20 juni 2024 13:30 t/m 16:45

A seminar on Logic, Set Theory, Topology

An afternoon of talks in honour of KP Hart's retirement

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