Design of Dynamic experiments with Functional Data.

这项研究涉及两个主要方面。实验设计（DoE）和功能数据分析（FDA）方法。DoE感兴趣的是在尚未发现物理定律的情况下，寻找优化实验以优化一个变量。这意味着结果变量无法轻易优化，因为还不存在需要优化的功能。DoE方法创建了一个线性模型来近似真实的潜在物理定律，并创建了一个设计（多个实验），可以智能地搜索特征空间，而无需显式地搜索所有可能性。FDA是一种适用于各种类型数据的方法，但主要适用于时间序列数据和空间数据（除天气模式外）。这种分析背后的基本思想是，我们假设所讨论的变量在其各自的域中是真正连续的。我们可以在不同的时间或空间间隔内对其进行采样，但实际上变量从一种状态平滑地过渡到另一种状态。我的研究重点是什么是一个实验的最佳设计，当变量的特征被优化，甚至结果本身可以被认为是一个功能变量。除此之外，我们还致力于开发一种新的算法来解决上述问题。这个项目是我们目前的重点。为了用传统算法解决这些问题，需要大量的时间，因此我们开始致力于开发更现代、更快的算法。

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.