BUC-V: Uncertainty quantification: When PDEs meet data science (Bath) 

20-23 September, University of Bath, 
Maths building (4West) Room 1.7 (Wolfson Lecture theatre)


Download programme

University Guide (Travel info and Wifi access)

UQ methods applied to ice cap modelling in the Antartic (generated by Omar Ghattas)


BUC-V is the fifth in the series of workshops with the theme of Uncertainty Quantification. It will be held in Bath. As with previous BUCs, there will be a short-course complemented by a series of talks by PhD students and young researchers, as well as a few invited talks by specialists. The short course will be on "Computation for Bayesian models of inverse problems in PDEs” and it will be given by the Bath IMI Global Chair Prof. Colin Fox from the University of Otago (NZ), a world-expert on MCMC methods for large-scale engineering applications.

Challenges posed by engineering, geology, weather, climate, biological and medical sciences (just to mention a few) have lead to a surge in the interest and development of two seemingly unrelated approaches:

  • large-scale statistical models to understand big datasets
  • efficient uncertainty quantication methods for complex applications

Even when these two general approaches are combined via (for example) data assimilation, filtering or Bayesian approaches, the state-of-the-art methods are either too inaccurate for many applications or too costly to study realistic situations. The focus of this workshop will be on novel methods that combine state-of-the-art statistical tools with cutting-edge numerical methods that can be brought to bear on real, large-scale applications.

Andrés Christian explains what an Uncertainty Quantification scientist looks like:
"A frankenstein made up of different body parts"

Short Course on "MCMC for Inverse Problems in PDEs"

Professor Colin Fox (University Otago)

Link to lecture notes

This short course will cover some first steps in performing computational sample-based inference in inverse problems where the forward map requires solving a PDE (partial differential equation). We will look at some MCMC (Markov chain Monte Carlo) algorithms for drawing samples that are distributed according to the resulting posterior distribution, in few and many dimensions, from simple to state of the art. We will also introduce some basic PDE solvers, and discuss the important finite-rank property of the associated forward map. In the last lecture we will discuss mid-level and high-level models, that are the future of this field. The accompanying practical computer sessions allows participants to get hands-on experience with all these topics.

Bath Institute for Mathematical Innovation (IMI) has appointed Professor Fox as Global Chair for the next academic year. He is an expert in MCMC methods for large-scale engineering applications.


Download programme

BUC-V participants

Tuesday (September 20)

12:00 - 13:00 Lunch                                                                   
13:00 - 13:45 Alex Beskos (UCL) - Multilevel Sequential Monte Carlo


13:45 - 14:45

Cesar Almenara (CIMAT) - Regularization and Prior Elicitation for Generalized Linear Models

Nico Kuschinski-Kathmann (CIMAT) - Bayesian experimental design for OGTT diagnosis of diabetes

14:45 - 15:15 Coffee
15:15 - 17:15

Tim Dodwell (Exeter) - Adaptive Multilevel Monte Carlo

Matt Parkinson (Bath) - Novel Monte Carlo Approaches for Uncertainty Quantification with Application to Neutron Transport

Gianluca Detommaso (Bath) - Multilevel DILI MCMC Algorithm

Sergey Dolgov (Bath) - Alternating Least Squares and Low-Rank Cross Approximation for Parametric PDEs


Wednesday (September 21)

09:30 - 11:00   Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Lecture)                                                  
11:00 - 11:30 Coffee
11:30 - 12: 30 Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Lecture)
12:30 - 13:30 Lunch
13:30 - 14:30 Colin Fox (Otago) MCMC for Inverse Problems (Practical)
14:30 - 15:15  Jonty Rougier (Bristol)  Uncertainty in the Boundary Conditions: Upscaling and Downscaling Digital Elevation Maps
15:15 - 15:45  Coffee
15:45 - 17:15

Silvia Gazzola (Bath) -  Krylov-Tikhonov methods for large-scale inverse problems

Ander Biguri (Bath) - TIGRE: software for iterative reconstruction algorithms in 3D X-ray

Marcos Capistrán (CIMAT) - An inverse problem arising in reflection and transmission of waves by functionally graded materials


Thursday (September 22)

09:30 - 11:00  Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Lecture)                                               
11:00 - 11:30 Coffee
11:30 - 12: 30 Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Lecture)
12:30 - 13:30 Lunch
13:30 - 14:30 Colin Fox (Otago) MCMC for Inverse Problems (Practical)
14:30 - 15:15  Andrés Christen (CIMAT) - Numerical posterior distribution error control and expected Bayes Factors in the Bayesian Uncertainty Quantification of Inverse Problems
15:15 - 15:45  Coffee
15:45 - 17:15

Nathan Owen (Exeter) - Comparison of surrogate-based uncertainty quantification methods for computationally expensive simulators

Kari Heine (UCL) - Adapting Particle Filters to Parallel Architectures - Convergence and Fluctuations

Antonio Capella (UNAM) - Super Resolution in Atomic and Molecular Spectroscopy for Noisy Signals


Friday (September 23)

9:30 - 11:00 Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Lecture)                                     
11:00 - 11:30 Coffee
11:30 - 12:30 Colin Fox (Otago) MCMC for Inverse Problems in PDEs (Practical)
12:30 - 14:00 Lunch
14:00 - 16:00 Round Table of BUC Members

Further Details

The workshop forms part of the joint IMI/SAMBa Thematic Semester on Markov Chain Monte Carlo Methods and is financially supported by the Bath Institute for Mathematical Innovation, by EPSRC through the SAMBa CDT and by the University of Bath Internationalisation Fund.

Other information

University Guide (Travel info and Wifi access)


Rob Scheichl
Karim Anaya-Izquierdo 
Eike Muller
Daniel Simpson
Silvia Gazzola
Sergey Dolgov
Gianluca Detommaso
Matthew Parkinson
Ander Biguri 
Melina Freitag 
Ivan Graham 
Tony Shardlow 
Anne Reinarz 
Victor Bayona 
Grigoris Katsiolides
Jonathan Dawes
James Fidal
James Hook
Andreas Kyprianou
Andrea Lelli
Owen Pembery
Gavin Shaddick


Andrés Christen (CIMAT)
Nico Kuschinski-Kathmann (CIMAT)
Marcos Capistran (CIMAT)
Juan-Carlos Pardo (CIMAT)
Cesar Almenara (UNAM)
Antonio Capella (UNAM)
Colin Fox (Otago)
Alex Beskos (UCL)
Jonty Rougier (Bristol)
Tim Dodwell (Exeter)
Nathan Owen (Exeter)
Kari Heine (UCL)
Abdul-Lateef Haji-Ali (Oxford)
Jim Zidek (UBC, IMI Chair)