By Jennifer Scott and Kirk M. Soodhalter
The 26th Annual Meeting of the SIAM United Kingdom and Republic of Ireland (UKIE) Section took place on January 7, 2022. SIAM UKIE president Jennifer Scott (University of Reading and the Science and Technology Facilities Council), vice president Kirk M. Soodhalter (Trinity College Dublin), and secretary/treasurer Francesca Arrigo (University of Strathclyde) organized the conference, and Trinity College Dublin served as the meeting’s virtual host. Though we originally intended for the festivities to commence in person, the sudden arrival of COVID-19’s Omicron variant and the resulting spike in cases meant that we regretfully had to switch to a virtual event. However, the online format widened access to the conference and enabled the participation of attendees who otherwise would not have been able to travel to Dublin.
More than 60 registered participants attended the conference talks, which highlighted advances in deep learning, weather simulation, numerical linear algebra, data assimilation, and inverse problems. The five invited speakers were David Barrett (Google Deepmind), Sarah Dance (University of Reading), Marco Marletta (Cardiff University), John Pearson (University of Edinburgh), and Valeria Simoncini (University of Bologna). Rather than host our usual lunchtime poster event, six Ph.D. students from different universities around the U.K. and Ireland delivered 10-minute talks about their respective projects; these talks afforded the students important early-career experience in presenting and facilitated networking opportunities. Another nice feature of the day was the use of informal, randomly assigned Zoom breakout rooms during coffee breaks, which allowed attendees to chat and network in brief increments. Additionally, a pre-recorded statutory business meeting and financial discussion of the SIAM UKIE Section was made available to all section members.
Barrett’s talk—intriguingly titled “The Geometric Occam Razor Implicit in Deep Learning”—outlined new mathematical insights that explain the surprising effectiveness of several deep learning algorithms in domains as diverse as image classification and language translation. Barrett used backward error analysis to reveal a hidden built-in mechanism called implicit gradient regularization that guides deep learning towards solutions with low geometric model complexity.
Dance spoke about “Making the Most of Observations in Numerical Weather Prediction: A Large Nonlinear Least-squares Problem.” She discussed the ability of mathematical weather simulations to update real-time weather data and improve forecasts by solving a large nonlinear weighted least-squares problem, wherein the model and observational data are weighted by their respective uncertainties. She also presented recent research about the characterization and treatment of observation uncertainty in assimilation systems.
Marletta’s presentation on “An Inverse Problem in Electromagnetism with Partial Data” addressed the feasibility of determining unique permeability, permittivity, and conductivity in a domain’s time-harmonic Maxwell system by taking certain measurements of electric and magnetic fields on only a small, open subset of the boundary.
Pearson considered “Numerical Methods and Linear Algebra for PDE-Constrained Optimization Problems.” These problems arise in a huge range of practical applications, including fluid flow control, medical imaging, biological and chemical processes, and electromagnetic inverse problems. Pearson introduced general computational strategies for the solution of such problems with an all-at-once approach; these types of strategies lead to large-scale linear systems that one can solve via Krylov subspace methods that are paired with robust levels of preconditioning.
Finally, in a talk entitled “Computational Methods for Large-scale Matrix Equations and Application to PDEs,” Simoncini discussed the numerical treatment of large-scale Lyapunov and Sylvester equations and their generalizations via projections onto Krylov subspaces. These equations are important in dynamical systems, control theory, and eigenvalue computation, but they have recently been recognized in the discretization of partial differential equations (PDEs) — particularly stochastic PDEs.
We hope that Trinity College Dublin can host the 2023 SIAM UKIE Annual Meeting in person next year, provided that the COVID-19 pandemic allows such an event to occur. However, we will plan to include a virtual component for those who cannot travel to Dublin in order to bolster conference access for prospective attendees.
Jennifer Scott is a professor of applied mathematics at the University of Reading and Director at Reading of the Mathematics of Planet Earth Centre for Doctoral Training. She is also a Research Fellow at the Science and Technology Facilities Research Council and president of the UKIE Section of SIAM. Kirk M. Soodhalter is the Ussher Assistant Professor in Numerical Analysis at Trinity College Dublin. He is vice president of the UKIE Section of SIAM.