Stochastic Numerics and Inverse Problems

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Stochastic Numerics and Inverse Problems

 Jun 09 2021

13:00 - 14:00

Organisers:


  • Charles-Edouard Bréhier, CNRS & Université Lyon 1

  • Evelyn Buckwar, Linz University

  • Erika Hausenblas, Loeben University

  • Ray Kawai, Tokyo University

  • Gabriel Lord, Radboud University

  • Mikhail Tretyakov, Nottingham University

  • Kostas Zygalakis, University of Edinburgh

This is a One World Seminar
. The seminars occur bi-weekly on a Wednesdays 13.00-14.00 BST

Zoom is the online platform being used to deliver this seminar series.

Register Here

Recordings from this seminar series are available here.


Future Seminars 

9 June 2021

Laura Scarbosio, Radboud University Shape uncertainty quantification for non-smooth quantities of interest

Abstract: In this talk I will focus on Helmholtz interface problems with uncertain interface as an example where some quantities of interest, such as point values of the solution, depend non-smoothly on the parameter describing the shape variations. The non-smoothness poses a challenge for classical uncertainty quantification methods, due to the high-dimensionality of the parameter space. I will show that, if one is interested in the average of the quantity of interest, then multilevel Monte Carlo is a robust and viable algorithm. If one is interested instead in a surrogate of the parameter-to-quantity of interest map, this can be built using deep neural networks with ReLU activation function. I will provide a theoretical justification for why one can expect these neural networks to be good candidates for a surrogate, and I will show numerical results illustrating their performance in dependence of different modeling parameters.


23 June 2021

Annika Lang, Chalmers University 

7 July 2021

Gabriel Stoltz, Ecole des Ponts

Previous Seminars


Erika Hausenblas, Montanuniversitaet Leoben: Stochastic Activator-Inhibitor models and its Numerical Modelling

Monika Eisenmann, Lund University - Sub-linear convergence of stochastic optimization methods in Hilbert space


Konstantinos Dareiotis, University of Leeds - Approximation of stochastic equations with irregular drifts

  • This seminar was NOT recorded 


 

Andrew Stuart, Caltech - Inverse Problems Without Adjoints


Svetlana Dubinkina, Vrije Universiteit Amsterdam - Shadowing approach to data assimilation

 

Denis Talay, Inria and Ecole Polytechnique - Probability distributions of first hitting times of solutions to SDEs w.r.t. the Hurst parameter of the driving fractional Brownian noise: A sensitivity analysis

 

Evelyn Buckwar, Johannes Kepler University - A couple of ideas on splitting methods for SDEs

 

Andreas Prohl, Tübingen - Numerical methods for stochastic Navier-Stokes equations


 

Mireille Bossy, INRIA - SDEs with boundaries, modelling particle dynamics in turbulent flow


 

Raphael Kruse, Halle-Wittenberg - On the BDF2-Maruyama method for stochastic evolution equations 


 

Adrien Laurent, University of Geneva - Order conditions for sampling the invariant measure of ergodic stochastic differential equations in R^d and on manifolds


 

Chuchu Chen, Chinese Academy of Sciences - Probabilistic superiority of stochastic symplectic methods via large deviations principle


  • This seminar was NOT recorded


Kostas Zygalakis, University of Edinburgh - Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems


 

Xuerong Mao, Strathclyde - The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations

 

Charles-Edouard Bréhier, Claude Bernard Lyon - Analysis of splitting schemes for the stochastic Allen-Cahn equation

 

Conall Kelly, University College Cork - A hybrid, adaptive numerical method for the Cox-Ingersoll-Ross model


 

Abdul Lateef Haji-Ali, Heriot Watt University - Sub-sampling and other considerations for efficient risk estimation in large portfolios


 

David Cohen, Umeå University - Drift-preserving schemes for stochastic Hamiltonian and Poisson systems


 

Gabriel Lord, Radboud University - Numerics and SDE a model for the stochastically forced vorticity equation


 

Marco Iglesias, University of Nottingham - Ensemble Kalman Inversion: from subsurface environments to composite materials

 

Ray Kawai, University of Tokyo - Stochastic approximation in adaptive Monte Carlo variance reduction


  • This seminar was NOT recorded


Kody Law, University of Manchester - Bayesian Static Parameter Estimation using Multilevel and multi-index Monte Carlo


 

Akash Sharma & Michael Tretyakov, University of Nottingham - Computing ergodic limits of reflected diffusions and sampling from distributions with compact support


 

Georg Gottwald, The University of Sydney - Simulation of non-Lipschitz stochastic differential equations driven by α-stable noise: a method based on deterministic homogenisation


 

Marta Sanz-Sole, Barcelona - Global existence for stochastic waves with super-linear coefficients


 

Sonja Cox, University of Amsterdam - Efficient simulation of generalized Whittle-Mat'ern fields

 

This seminar series is supported as part of the ICMS Online Mathematical Sciences Seminars.