Numerical Analysis Group Internal Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
22 October 2019
14:00
Yufei Zhang
Abstract

In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the H^2 -norm, and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem and the perpetual American option pricing problems are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
 

  • Numerical Analysis Group Internal Seminar
22 October 2019
14:30
James Foster
Abstract

In this talk, I will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. Most notably, the coefficients obtained from this expansion are independent Gaussian random variables. This will enable us to generate approximate Brownian paths by matching certain polynomial moments. To conclude the talk, I will discuss related works and applications to numerical methods for SDEs.
 

  • Numerical Analysis Group Internal Seminar
29 October 2019
14:30
Priya Subramanian
Abstract

Complex spatial patterns such as superlattice patterns and quasipatterns occur in a variety of physical systems ranging from vibrated fluid layers to crystallising soft matter. Reduced order models that describe such systems are usually PDEs. Close to a phase transition, modal expansion along with perturbation methods can be applied to convert the PDEs to normal form equations in the form of coupled ODEs. I use equivariant bifurcation theory along with homotopy methods (developed in computational algebraic geometry) to obtain all solutions of the normal form equations in a non-iterative method. I want to talk about how this approach allows us to ask new questions about the physical systems of interest and what extensions to this method might be possible. This forms a step in my long-term interest to explore how to better ‘complete’ a bifurcation diagram!

  • Numerical Analysis Group Internal Seminar
5 November 2019
14:00
Maha Kaouri
Abstract

The variational data assimilation (VarDA) problem is usually solved using a method equivalent to Gauss-Newton (GN) to obtain the initial conditions for a numerical weather forecast. However, GN is not globally convergent and if poorly initialised, may diverge such as when a long time window is used in VarDA; a desirable feature that allows the use of more satellite data. To overcome this, we apply two globally convergent GN variants (line search & regularisation) to the long window VarDA problem and show when they locate a more accurate solution versus GN within the time and cost available.
Joint work with Coralia Cartis, Amos S. Lawless, Nancy K. Nichols.

  • Numerical Analysis Group Internal Seminar
5 November 2019
14:30
Sophy Oliver
Abstract

Ocean biogeochemical models used in climate change predictions are very computationally expensive and heavily parameterised. With derivatives too costly to compute, we optimise the parameters within one such model using derivative-free algorithms with the aim of finding a good optimum in the fewest possible function evaluations. We compare the performance of the evolutionary algorithm CMA-ES which is a stochastic global optimization method requiring more function evaluations, to the Py-BOBYQA and DFO-LS algorithms which are local derivative-free solvers requiring fewer evaluations. We also use initial Latin Hypercube sampling to then provide DFO-LS with a good starting point, in an attempt to find the global optimum with a local solver. This is joint work with Coralia Cartis and Samar Khatiwala.
 

  • Numerical Analysis Group Internal Seminar
12 November 2019
14:00
Ioannis Papadopoulos
Abstract

Topology optimisation finds the optimal material distribution of a fluid or solid in a domain, subject to PDE and volume constraints. There are many formulations and we opt for the density approach which results in a PDE, volume and inequality constrained, non-convex, infinite-dimensional optimisation problem without a priori knowledge of a good initial guess. Such problems can exhibit many local minima or even no minima. In practice, heuristics are used to obtain the global minimum, but these can fail even in the simplest of cases. In this talk, we will present an algorithm that solves such problems and systematically discovers as many of these local minima as possible along the way.  

  • Numerical Analysis Group Internal Seminar

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