Optimal control problems in mathematical biology: Modelling, analysis and numerics

点击翻译按钮获取中文摘要

Many of the mechanisms governing pattern formation in embryonic development have been identified and described by systems of PDEs. As some of the parameters or functions in these PDEs may be impossible to measure in laboratory conditions, we can use optimal control theory, in particular PDE-constrained optimization, to identify them. In my project, I'm devising fast numerical solvers for PDEs that arise from PDE-constrained optimisation problems. In the optimisation problem, the unknown parameter or function in the model is set to be the control variable. Using fast numerical solvers and experimental data (e.g. an image), we can identify the control to complete the model. So far, I have dealt with reaction-diffusion equations, however, I'm currently working on more challenging problems that involve chemotaxis, i.e. movement of cells up or down chemical gradients.