When solving PDEs, we often assume that many quantities such as boundary conditions, coefficients, forcing terms are fixed and known. That is hardly the case in practice, as you often need to estimate them, with limited data and uncertainty on measurements. As it turns out, statisticians have been solving this kind of problems for a long time, albeit with different notation and language.
In this talk we will take a look at how to estimate coefficients of a PDE, in the context of Uncertainty Quantification, from the point of view of Statisticians. Hopefully this will significantly expand the amount of useful literature you can rely on, for either research or a job in the private sector.