Jemima Tabaert

Title: Numerical linear algebra for weather forecasting

Abstract: The quality of a weather forecast is strongly determined by  the accuracy of the initial condition. Data assimilation methods allow us to combine prior forecast information with new measurements in order  to obtain the best estimate of the true initial condition. However, many of these approaches require the solution an enormous least-squares problem. In this talk I will discuss some mathematical and computational challenges associated with data assimilation for numerical weather prediction, and show how structure-exploiting numerical linear algebra approaches can lead to theoretical and computational improvements.


Babette de Wolff

Title: Phase reduction for networks of delay-coupled oscillators
Abstract: In many real-life networks systems, it takes a significant time for signals to travel from node to node, leading to time delays in the coupling. Experiments show that coupling delays have a crucial and often counterintuitive effect on collective phenomena, including the synchronisation behaviour of coupled oscillators.

In this talk, I will introduce a phase reduction technique for delay-coupled oscillators, which gives a systematic way to derive equations for the phases of coupled oscillators. The resulting phase model is lower dimensional than the original model (in fact, it is finite dimensional while the original model is infinite dimensional), which facilitates further analysis of synchronisation phenomena.

I will first discuss the mathematical approach to phase reduction in delay-coupled oscillators, including the approach to compute higher-order terms (i.e. terms of order at least 2) in the coupling parameter. By means of an illustrative example, I will then show how including these higher-order terms yields more accurate predictions of synchronisation behaviour.


Chiheb Ben Hammouda

Title: Automated Importance Sampling via Optimal Control for Stochastic Reaction Networks: Learning and Markovian Projection-based Approaches

Abstract: Stochastic reaction networks (SRNs) are a particular class of continuous-time Markov chains used to model a wide range of phenomena, including biological/chemical reactions, epidemics, risk theory, queuing, and supply chain networks. In this context, we explore the efficient estimation of statistical quantities, particularly rare event probabilities, and propose two alternative importance sampling (IS) approaches [1,2] to improve the Monte Carlo (MC) estimator efficiency. The key challenge in the IS framework is to choose an appropriate change of probability measure to achieve substantial variance reduction, which often requires insights into the underlying problem. Therefore, we propose an automated approach to obtain a highly efficient path-dependent measure change based on an original connection between finding optimal IS parameters and solving a variance minimization problem via a stochastic optimal control formulation. We pursue two alternative approaches to mitigate the curse of dimensionality when solving the resulting dynamic programming problem. In the first approach [1], we propose a learning-based method to approximate the value function using a neural network, where the parameters are determined via a stochastic optimization algorithm. As an alternative, we present in [2] a dimension reduction method, based on mapping the problem to a significantly lower dimensional space via the Markovian projection (MP) idea. The output of this model reduction technique is a low dimensional SRN (potentially one dimension) that preserves the marginal distribution of the original high-dimensional SRN system. The dynamics of the projected process are obtained via a discrete $L^2$ regression. By solving a resulting projected Hamilton-Jacobi-Bellman (HJB) equation for the reduced-dimensional SRN, we get projected IS parameters, which are then mapped back to the original full-dimensional SRN system, and result in an efficient IS-MC estimator of the full-dimensional SRN. Our analysis and numerical experiments verify that both proposed IS (learning based and MP-HJB-IS) approaches substantially reduce the MC estimator’s variance, resulting in a lower computational complexity in the rare event regime than standard MC estimators.

[1] Ben Hammouda, C., Ben Rached, N., and Tempone, R., and Wiechert, S. Learning-based importance sampling via stochastic optimal control for stochastic reaction net-works. Statistics and Computing 33, no. 3 (2023): 58.
[2] Ben Hammouda, C., Ben Rached, N., and Tempone, R., and Wiechert, S. (2023). Automated Importance Sampling via Optimal Control for Stochastic Reaction Networks: A Markovian Projection-based Approach.  arXiv preprint arXiv:2306.02660.


Havva Yoldas

Title: Quantitative hypocoercivity results for kinetic equations in mathematical biology

Abstract: After a short introduction on kinetic equations and classical $L^2/H^1$ hypocoercivity techniques due to Dolbeault, Mouhot, Schmeiser AMS 2015, I will talk about Harris-type theorems that is an alternative method for obtaining quantitative convergence rates. I will discuss how to use these theorems summarising some recent results obtained jointly with Jo Evans (Warwick) on the run and tumble equations that is a kinetic-transport equation modelling the bacterial movement under the effect of a chemoattractant.