Design of Dynamic experiments with Functional Data.

The research involves two major axis. The Design of Experiments (DoE) and the Functional Data Analysis (FDA) methodologies.
DoE is interested in finding optimal experiments in order to optimise one variable, when a physical law has not beed discovered yet. This means that the outcome variable cannot be optimised easily as there exist no function to be optimised yet. The DoE methodology creates a linear model to approximate the true underlying physical law and creates a design (multiple experiments) that intelligently searched the feature space without the need to explicitly search all the possibilities.
FDA is a methodology that is applied to various types of data, but mainly on time series data as well as space data (ex weather patterns). The basic idea behind this type of analysis is that we assume that our variable in question is truly continuous in its respective domain. We might sample it in distinct time or space intervals but in reality the variable smoothly transitioned from one state to the next.

My research focuses on what would an optimal design for an experiment be, when the features of the variable to be optimised, or even the outcome itself can be considered a functional variable.

In addition to those, we are also working towards developing a new algorithm to solve the above problem. This project is currently our main focus. In order to solve these kinds of problems with traditional algorithm, a major amount of time was needed and hence we started working towards developing a more modern and faster algorithm.