# Manchester SIAM-IMA Student Chapter Conference
## 2023

Xinye Chen, Xiaobo Liu, Ioanna Nikolopoulou, Alban Bloor Riley, Bastien

Vieublé, Zhengbo Zhou

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► To cite this version:

Xinye Chen, Xiaobo Liu, Ioanna Nikolopoulou, Alban Bloor Riley, Bastien Vieublé, et al. Manchester SIAM-IMA Student Chapter Conference 2023. Manchester SIAM-IMA Student Chapter Conference 2023, Apr 2023, Manchester, United Kingdom. 2023. [hal-05321776](https://hal.science/hal-05321776v1)

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Manchester SIAM-IMA Student
Chapter Conference 2023

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Programme and Abstract Booklet

27 April 2023

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The organisers

Xinye Chen

Xiaobo Liu

Ioanna Nikolopoulou

Alban Bloor Riley

Bastien Vieuble

Zhengbo Zhou
# Programme

<table><tr><td>08:30 - 09:00</td><td>Registration</td></tr><tr><td>09:00 - 09:05</td><td>Opening of the conference</td></tr><tr><td>09:05 - 09:25</td><td>Student talk by Benjamin Kent</td></tr><tr><td>09:25 - 10:25</td><td>Invited talk by Chris Armstrong</td></tr><tr><td>10:25 - 10:50</td><td>Coffee break</td></tr><tr><td>10:50 - 11:50</td><td>Invited talk by Mantas Mikaitis</td></tr><tr><td>11:50 - 12:10</td><td>Student talk by Efthymia Derezea</td></tr><tr><td>12:10 - 12:30</td><td>Student talk by Frank Millward</td></tr><tr><td>12:30 - 12:50</td><td>Student talk by Yubo Rasmussen</td></tr><tr><td>12:50 - 13:00</td><td>Group photo</td></tr><tr><td>13:00 - 14:00</td><td>Lunch break</td></tr><tr><td>14:00 - 15:00</td><td>Invited talk by Marta Catalano</td></tr><tr><td>15:00 - 15:20</td><td>Student talk by Hollie Lloyd</td></tr><tr><td>15:20 - 15:40</td><td>Student talk by Daniel McKinnell</td></tr><tr><td>15:40 - 16:00</td><td>Coffee break</td></tr><tr><td>16:00 - 17:00</td><td>Invited talk by Ricardo Silva</td></tr><tr><td>17:00 - 17:10</td><td>Prizes and closing</td></tr><tr><td>17:10</td><td>Informal outing</td></tr></table>
Invited Talks

Invited Talk I
Frank Adams 1-2
09:25 - 10:25

Optimizing Numerical Libraries

Chris Armstrong
Arm Manchester

Manchester is home to Arm's second largest office in the UK, and also home to the team of numerical software developers I work with. We optimize code running on Arm systems which serve a range of different domains, and in this talk I will give an overview of what optimization means in each of the products we deliver.

Invited Talk II
Frank Adams 1-2
10:50 - 11:50

Stochastic Rounding: Implementation, Error Analysis and Applications

Mantas Mikaitis
School of Computing, University of Leeds

Stochastic rounding (SR) randomly maps a real number $x$ to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to $x$. This rounding mode was first proposed for use in computer arithmetic in the 1950s and it is currently experiencing a resurgence of interest. In this talk we will review the main results from our recent survey paper on SR (R. Soc. Open Sci. 9:3), including the basic properties, error analysis, applications, and implementation of SR in the context of floating-point arithmetic.
# Measuring the Impact of the Prior in Bayesian Nonparametrics via Optimal Transport

Marta Catalano

Department of Statistics, University of Warwick

Invited Talk III
Frank Adams 1-2
14:00 - 15:00

The Bayesian approach to inference is based on a coherent probabilistic framework that naturally leads to principled uncertainty quantification and prediction. Via conditional (or posterior) distributions, Bayesian nonparametric models make inference on parameters belonging to infinite-dimensional spaces, such as the space of probability distributions. The development of Bayesian nonparametrics has been triggered by the Dirichlet process, a nonparametric prior that allows one to learn the law of the observations through closed-form expressions. Still, its learning mechanism is often too simplistic and many generalizations have been proposed to increase its flexibility, a popular one being the class of normalized completely random measures. Here we investigate a simple yet fundamental matter: will a different prior actually guarantee a different learning outcome? To this end, we develop a new distance between completely random measures based on optimal transport, which provides an original framework for quantifying the similarity between posterior distributions (or merging of opinions). Our findings provide neat and interpretable insights on the impact of popular Bayesian nonparametric priors, with very mild assumptions on the data-generating process. This is joint work with Hugo Lavenant.

# Stochastic Causal Programming for Bounding Treatment Effects

Ricardo Silva

Department of Statistical Science, University College London

Invited Talk IV
Frank Adams 1-2
16:00 - 17:00

Causal effect estimation is important for numerous tasks in the natural and social sciences. However, identifying effects is impossible from observational data without making strong, often untestable assumptions. We consider algorithms for the partial identification problem, bounding treatment effects from multivariate, continuous treatments over multiple possible causalmodels when unmeasured confounding makes identification impossible. We consider a framework where observable evidence is matched to the implications of constraints encoded in a causalmodel by norm-based criteria. This generalizes classical approaches based purely on generative models. Casting causal effects as objective functions in a constrained optimization problem, we combine flexible learning algorithms with Monte Carlo methods to implement a family of solutions under the name of stochastic causal programming. In particular, we present ways by which such constrained optimization problems can be parameterized without likelihood functions for the causal or the observed data model, reducing the computational and statistical complexity of the task.

Joint work with Kirtan Padh, Jakob Zeitler, David Watson, Matt Kusner and Niki Kilbertus.
Student Talks

Student Talk I
Frank Adams 1-2
09:05 - 09:25

Efficient Adaptive Stochastic Collocation Strategies for
Advection-Diffusion Problems with Uncertain Inputs

Benjamin Kent

Department of Mathematics, The University of Manchester

Physical models with uncertain inputs are commonly represented as parametric
partial differential equations (PDEs). That is, PDEs with inputs that are expressed
as functions of parameters with an associated probability distribution. Developing
efficient and accurate solution strategies that account for errors on the space, time
and parameter domains simultaneously is highly challenging. Indeed, it is well
known that standard polynomial-based approximations on the parameter domain
can incur errors that grow in time. In this work, we focus on advection-diffusion
problems with parameter-dependent wind fields. A novel adaptive solution strategy
is proposed that allows users to combine stochastic collocation on the parameter
domain with off-the-shelf adaptive timestepping algorithms with local error control.
This is a non-intrusive strategy that builds a polynomial-based surrogate that is
adapted sequentially in time. The algorithm is driven by a so-called hierarchical
estimator for the parametric error and balances this against an estimate for the
global time-stepping error which is derived from a scaling argument.

Student Talk II
Frank Adams 1-2
11:50 - 12:10

An Application of Saddlepoint Approximation for Period Detection of
Astronomical Light Curves

Efthymia Derezea

School of Mathematics, University of Bristol

One of the main features of interest in analysing the light curves of stars is the
underlying periodic behaviour. The corresponding observations are a complex type
of time series with unequally spaced time points. The main tools for analysing
these type of data rely on the periodogram-like functions, constructed with a desired
feature so that the peaks indicate the presence of a potential period. We explore a
particular periodogram for the irregularly observed time series data. We identify the
potential periods by implementing the saddlepoint approximation, as a faster and
more accurate alternative to the simulation based methods that are currently used.
The power analysis of the testing methodology is reported together with applications
using light curves from the Hunting Outbursting Young Stars citizen science project.
# Modelling Wind-Blown Umbrella Clouds

Frank Millward

Department of Mathematics, The University of Manchester

Student Talk III
Frank Adams 1-2
12:10 - 12:30

Erupting volcanoes eject a mixture of hot gas and ash which rises through the stratified atmosphere as a convective plume to its neutral buoyancy level: the height at which the density of the ash-gas mix is equal to that of the surrounding atmosphere. At this height, the plume ceases rising vertically and instead spreads laterally, driven by buoyancy forces. This giant laterally spreading structure is known as an umbrella cloud. Producing faster than real-time predictions of ash spread is vital for the aviation industry, as ash can cause accelerated engine wear or even failure in jet aircraft. These predictions are produced by Volcanic Ash Transport and Dispersion Models (VATDMs), which use the outputs of Numerical Weather Prediction (NWP) models to simulate the dispersion of ash by turbulent diffusion and atmospheric wind. Historically, VATDMs have neglected buoyancy forces, under the assumption that dispersion is dominated by wind advection and turbulent diffusion. For large eruptions, VATDMs can significantly underestimate the spread of ash, suggesting this assumption may not be valid. In this talk, we introduce a new parametrisation of buoyancy-driven spreading which is based on a shallow-layer model of umbrella clouds. This non-axisymmetric parametrisation can accurately describe the interaction between buoyancy and atmospheric wind. While it incorporates much of the complex physics governing the spread of umbrella clouds, the parametrisation remains fast enough for operational use in a VATDM. The parametrisation is validated in the Met Office's NAME VATDM and shown to improve predictions of ash spread for the historic eruption of Puyehue-Cordón Caulle, Chile, in 2011.

# Neural Network Embedding of the Pareto Regression Model for Claims Severity

Yubo Rasmussen

School of Mathematical and Computer Sciences, Heriot-Watt University

The Pareto regression model has been widely used by the actuarial community for predicting claim sizes based on important risk factors in non-life insurance. The aim of this paper is to extend the framework of this model by embedding it into a Neural Network architecture following the Combined Actuarial Neural Network (CANN) from Wüthrich and Merz (2023). We exemplify our approach by implementing the blended model for fitting claim sizes from a European Motor Third Party Liability (MTPL) insurance company. We illustrate that the Neural Network boosting of the Pareto regression model enables us to explore missing interactions of nonmultiplicative type, that cannot be approximated by the Pareto regression model.

Student Talk IV
Frank Adams 1-2
12:30 - 12:50
# Continuum Modelling of a Granular Superstable Heap

Hollie Lloyd

Department of Mathematics, The University of Manchester

There are many advantages to having a predictive model for granular materials from both an industrial and geophysical perspective. The development of a rheological model which captures all granular behaviour remains a highly active area of research; complicated by the diverse behaviour granular systems exhibit. For flowing granular materials, a key development was the dependence of the granular inter-particle friction $\mu$ on the dimensionless inertial number $I$, and the functional form of this relationship known as the $\mu(I)$-rheology. In this rheology, granular materials can be modelled as an incompressible, viscoplastic fluid, where the viscosity depends on the inter-particle friction; this has been widely used with success. When investigating the behaviour of granular materials, oftentimes small scale experiments are used which are only a few grain diameters wide and confined by transparent sidewalls, from which experimental measurements are taken. The influence of these confining sidewalls is frequently neglected, when the effects of such a confinement are non-negligible. By implementing a width averaged sidewall friction force, this effect is accounted for in a two dimensional system. A granular superstable heap requires the successful implementation of wall friction forces in order to form, making it an appropriate test case to validate our model. In this work, numerical simulations are performed and compared with experimental and theoretical results to demonstrate its success.

# Depthwise Dependence in the Slowing Behaviour of Debris Flows

Daniel McKinnell

Department of Mathematics, The University of Manchester

Debris flows occur when particles of rock surrounded by water flow downhill. These flows originate on steep mouAntainous slopes but flow onto the shallower slopes of valley floors. High fluid pressures support much of the solid weight, which decreases friction and prolongs the flow, compared to flows without interstitial fluid. As the fluid pressure dissipates, the material deposits from the base up. Previous continuum models have taken a depth averaged approach which simplifies the problem but makes assumptions about velocity and pressure profiles in the depthwise direction, and is unable to describe the gradual deposition of material. We will present a 1-D model that includes variation throughout the flow height, identify timescales present in slowing and compare to previous depth averaged models.