## One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems

This is the webpage for the One World Stochastic Numerics and Inverse Problems Seminar Series

The organisers for the seminar series are: 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 (Edinburgh University)

The seminars occur weekly on a Wednesday (1pm British Summer Time (BST), 2pm Central European Summer Time (CEST))

### **Please note these seminars are currently on the summer break, and will be resuming in September 2020. **

### To sign up for this seminar series, please complete this form.

Recordings from this seminar series are available here.

### Future Seminar

September 9, 2020

Chuchu Chen(Chinese Academy of Sciences)Title:

Probabilistic superiority of stochastic symplectic methods via large deviations principle

Abstract: Plenty of numerical experiments show that stochastic symplectic methods are superior to non-symplectic ones especially in long-time computation, when applied to stochastic Hamiltonian systems. In this talk, we attempt to study the superiority of stochastic symplectic methods by means of the theory of large deviations. Concerning that the stochastic oscillator is one of the typical linear stochastic Hamiltonian systems, we take it as the test equation to obtain precise results about the rate functions of large deviations principles for both exact and numerical solutions. We prove that stochastic symplectic methods are able to asymptotically preserve the large deviations principles for both the mean position and mean velocity of exact solution, while non-symplectic ones do not. This indicates that stochastic symplectic methods are able to approximate well the exponential decay speed of the hitting probability.

September 23, 2020

Adrien Laurent(University of Geneva)Title:

Order conditions for sampling the invariant measure of ergodic stochastic differential equations in R^d and on manifoldsAbstract: For sampling the invariant measure of ergodic systems in large dimension, it is known that the order conditions are different from the standard weak order conditions over short time, and they can be intricate to compute. In this talk, we propose a new methodology, based on an extension of the exotic aromatic Butcher-series formalism, for constructing high order integrators for sampling the invariant measure of ergodic stochastic differential equations either in R^d or on manifolds

October 7, 2020

Mireille Bossy(INRIA)

October 21, 2020

Raphael Kruse(Halle-Wittenberg)

November 4, 2020

Marta Sanz-Sole(Barcelona)

November 18, 2020

TBC

December 02, 2020

Andreas Prohl(Tübingen)

December 16, 2020

Evelyn Buckwar(Johannes Kepler University)Title:

Structure preserving methods for a finite dimensional stochastic Landau-Lifshitz-Gilbert equationAbstract: In this talk we discuss a finite dimensional stochastic Landau-Lifshitz-Gilbert equation. The equation describes the precessional motion of the magnetisation of magnetic nanoparticles subject to thermal noise and comes with a number of features. In particular, the modulus if its solution is conserved over time and the expectation of the energy is bounded, these are features that need to be preserved in a numerical approximation. We discuss approaches of designing structure-preserving numerical methods in this setting.

### Previous Seminars

Speaker:

Kostas Zygalakis(Edinburgh)Title:

Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems

A recording of this seminar is avialable here.

Speaker:

Xuerong Mao(Strathclyde)Title:

The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations

A recording of this seminar is avialable here.

Speaker:

Charles-Edouard Bréhier(Claude Bernard Lyon)Title:

Analysis of splitting schemes for the stochastic Allen-Cahn equation

A recording of this seminar is available here.

Speaker:

Conall KellyUniversity College Cork

Title: A hybrid, adaptive numerical method for the Cox-Ingersoll-Ross model

A recording of this seminar is available here

Speaker:

Abdul Lateef Haji-Ali(Heriot Watt University)

Title: Sub-sampling and other considerations for efficient risk estimation in large portfolios

A recording of this seminar is available here

Speaker:

David Cohen(Umeå University)

Title:Drift-preserving schemes for stochastic Hamiltonian and Poisson systemsThis seminar was not recorded.

Speaker:

Gabriel Lord(Radboud University)Title:

Numerics and SDE a model for the stochastically forced vorticity equation

A recording of this seminar is avialable here.

Speaker:

Marco Iglesias(University of Nottingham)

Title: Ensemble Kalman Inversion: from subsurface environments to composite materials

A recording of this seminar is avialable here.

Speaker:

Ray Kawai(University of Tokyo)

Title: Stochastic approximation in adaptive Monte Carlo variance reductionThis talk was NOT recorded.

Speaker:

Kody Law(University of Manchester)

Bayesian Static Parameter Estimation using Multilevel and multi-index Monte Carlo

Speaker:

Akash Sharma & Michael Tretyakov(University of Nottingham)Title:

Computing ergodic limits of reflected diffusions and sampling from distributions with compact support

Speaker:

Georg Gottwald(The University of Sydney)Title:

Simulation of non-Lipschitz stochastic differential equations driven by α-stable noise: a method based on deterministic homogenisation

This is a One World Seminar.

Zoom is the online platform being used to deliver this seminar series. Any questions relating to the seminar, please contact liam.holligan@icms.org.uk

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