当下数据科学在各个领域中都起着越来越重要的作用，其本质为如何从随机样本出发对潜在的模型进行重构。而逼近理论尤其是径向基函数方法为多维、散乱数据的处理和学习提供了有力的工具。学习理论作为其新的延伸点成为了其中的核心方法。利用这些方法对未知或者难以求解的复杂动力系统(微分方程)的研究也开始受到更多关注。本项目的主要研究内容包括：首先，通过真实的物理、金融中的数据学习未知的微分方程，并在理论上探讨模型是否具有良好的恢复能力；进一步，直接学习得到微分方程的离散格式，探寻深度学习网络设计与动力系统的关系；并且，从数据驱动的思想出发得到一些已知复杂动力系统的数值解；最后，我们还将对数据驱动建模得到的一些混沌动力系统模型给出物理、统计上的分析解释。本项目将借助“数据加模型”的思想，将逼近论、复杂动力系统与学习理论结合，希望这样的交叉能引起更多数学领域对数据科学的研究，带来更多相关数学工具的产生和发展。

Data-science, which has become more and more important in varied fields nowadays, aims to reconstruct the underlying models from the random samples. The approximation theory, especially the radial basis function method, is a powerful tool to deal with the multi-dimensional and scattered data. As the extension of the approximation theory, the learning theory becomes the key method. Further, more attention has been paid on using these scientific computing methods to learn or solve the complex dynamical systems (differential equations). This project will focus on the following three points. Firstly, we will learn the potential dynamical systems by real data from physics and economics, and investigate the recovery capabilities of the models. Besides, the numerical discrete schemes of the differential equations are learned directly, which will help us to bridge the designing of the deep network with dynamical systems. Then solving some complex dynamical systems based on the idea of data-driven will be considered. At last, we will explore the physical and statistical interpretations for some chaotic systems obtained from the learning algorithms. The study of this project is based on the view of ‘model + data’. It is an interdisciplinary research, which consists of approximation theory, complex dynamical systems and learning theory. More related mathematical methods will be developed to improve the theoretical study of the data sciences.