Richard Wilkinson (University of Nottingham) – Adjoint-accelerated inference in linear systems

Abstract: Linear systems occur (e.g. Lx=f) throughout engineering and the sciences, notably as differential equations. In many cases the forcing function (f) for the system is unknown, and interest lies in using noisy observations of the system (y=Ax+e) to infer the forcing, as well as other unknown parameters. I will discuss our recent work that uses adjoints of linear systems to infer forcing functions modelled as Gaussian processes (GP). By using a truncated basis expansion, we can do conjugate Bayesian inference for the GP, in many cases, with substantially lower computation than would be required using alternative methods. I'll demonstrate the approach using an advection-diffusion model that arises in our attempts to model the spread of air pollution in Kampala, Uganda.