A probabilistic programming framework for scalable and automated inference in partial differential equation constrained Bayesian inverse problems
Project ID: 2228cd1289 (You will need this ID for your application)
Research Theme: Information and Communication Technologies
UCL Lead department: Computer Science
Lead Supervisor: Matt Graham
Project Summary:
Why is this research important: Partial differential equations (PDEs) are used to model phenomena in a wide range of applications - from the atmospheric and ocean models underlying weather forecasting and climate projections, to plasma physics simulations used to design fusion energy reactors. A common use for PDE models is solving inverse problems - estimating unknown variables in the model given observations. Bayesian inference offers a principled approach for combining models with data to produce probabilistic statements about unknowns. While much work has been done on developing inference algorithms for inverse problems, existing implementations are often model specific, hindering their adoption in real-world problems which often involve numerically intensive models that require deployment on high performance computing (HPC) systems.
Who will you be working with: This project will be based in UCL’s Advanced Research Computing Centre, a laboratory for research and innovation in computational science. The supervisory team combines expertise in Bayesian computation and finite element methods along with extensive experience in developing high quality research software, and running simulations at scale on HPC systems.
What will you be doing: The project will aim to develop an open-source probabilistic programming framework for PDE-constrained inverse problems, combining an interface for defining probabilistic assumptions on the model components, with general-purpose implementations of inference algorithms suitable for use on HPC systems and in high-dimensional latent spaces. You will have ample freedom to shape the project to your interests - for example developing novel automated inference methodology for inverse problems or investigating the use of machine learning surrogates for model components to speed up simulation and inference.
Who are we looking for: We are looking for applicants with a passion for and experience in scientific programming and mathematical modelling. Prior expertise in Bayesian computation and/or finite element methods would be beneficial but not essential.