LMS Inverse Day Nottingham: BIG inverse problems
By Dr Yves van Gennip; Lecturer in the School of Mathematical Sciences at the University of Nottingham
The GeoEnergy Research Centre helped to sponsor this event
On Monday 29 February 2016, in the stately Council Room of
the University of Nottingham’s Trent Building, some thirty mathematicians and
scientists gathered for a day of talks and posters about big inverse problems.
This one-day meeting was one of four London Mathematical Society (LMS) meetings
on inverse problems that are being held every year at various locations in the
UK.
In the words of the American mathematician Joseph Keller,
two problems are ‘inverses of one another if the formulation of each involves
all or part of the solution of the other. Often, for historical reasons, one of
the two problems has been studied extensively for some time, while the other is
newer and not so well understood. In such cases, the former problem is called
the direct problem, while the latter is called the inverse problem.’ (Keller,
1976) In practice such inverse problems often deal with reconstructing model
parameters from observations, where the generative process which produces the
observations from the parameters is (approximately) known. Nowadays, with ever
improving data collection technologies and methods, the number of observations
of a given process can be very large. Dealing with such big inverse problems
requires new mathematics, posing new theoretical questions and promising even
wider applicability.
The five speakers on the day represented well the diverse
range of topics and techniques that are captured under the banner of inverse
problems. Prof. Felix Herrmann (University of British Columbia) kicked off the
day with a talk about randomised sampling in exploration seismology. He was
followed by Dr. Natalia Bochkina (University of Edinburgh) who spoke about
Bayesian inverse problems under possibly missipecified
nonregular likelihood.
During the lunch, which was provided in the modern atrium of
the School of Mathematical Sciences, several posters were presented on diverse
topics ranging from probabilistic numerical methods for nonlinear partial
differential equations to motion correction in dynamic contrast enhanced
magnetic resonance imaging. Later in the afternoon a poster prize was awarded
to Lia De Simon for her poster on the quantification of the uncertainty in
thermal properties of walls by means of Bayesian inversion.
 |
| The winning poster - Quantifying the uncertainty in thermal properties of walls by means of Bayesian Inversion |
The high quality of posters and talks thus far, was
continued into the afternoon with three more interesting talks. Prof. Simon
Arridge (University College London) presented the computational aspects of
photoacoustic tomography. Matthew Dunlop spoke about hierarchical Bayesian
level set inversion, before Dr. Marcelo Pereyra closed the official part of the
day with a presentation about the fast
proximal Markov chain Monte Carlo method.
The success of the day was celebrated with a drink in campus
bar Mooch, but reconstructing an account of that academic endeavour is left as
an inverse problem for the reader.
The next LMS Inverse Day will take place during the British
Applied Mathematics Colloquium in Oxford on Friday 8 April 2016.
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