Dimensionality Reduction of High Dimensional Time Series based on Artificial Neural Network
Authors: Wang Yilin 
Published: December 2021

Abstract
Molecular dynamics is a molecular simulation method which relies on Newtonian mechanics to simulate the motion of molecular system. In this method, some differential equations are integrated, and the results of integration are further processed to obtain the trajectory or momentum evolution process of some particles controlled by dynamic equations, and the technology of extracting the equilibrium state, motion process or related properties of classical particle system can be used. Through molecular dynamics simulation, we can obtain a series of properties of the system, which are widely used in experimental verification, theoretical derivation and other scenarios. Because it can obtain the dynamic state of macromolecules to make up for the limitations of these properties, it is widely used in the study of transmembrane proteins, polypeptide chains and other systems in life sciences. Through the kinetic path reduction of these systems, we can intuitively understand the characteristics of molecular folding, molecular motion and specific binding, which can play a very important role in the study of proteins and peptides. However, due to the characteristics of high-dimensional time series obtained by molecular dynamics simulation, it is difficult for us to pay attention to the collective state or characteristic process of the whole system in a non-equilibrium state or slow process. This is due to the difficulty in data processing and the difficulty in obtaining its characteristic function. This makes it very difficult to study the dynamic process of the whole system, especially the dynamic process at the intermediate non-equilibrium moment. It is difficult to solve this kind of problem by conventional methods, and only a few special simple systems can be solved by experience. Therefore, it is of great significance to find a method to obtain the characteristic function of the system through the trajectory obtained by molecular dynamics, and then reduce the molecular dynamics path. In order to solve this scientific problem, researchers focus on machine learning. In this study, machine learning method will be used to solve the overall non-equilibrium state of the system or the collective state of the slow process in molecular dynamics simulation. Firstly, we use this method to solve a simple one-dimensional four well model. By this method, we obtain a series of characteristic functions describing the motion process of the model. By sorting the eigenvalue contributions, we obtain some main characteristic functions describing the system. It includes the motion description of Markov smooth transition state and the motion description of four potential wells. At the same time, we use the traditional transition probability matrix to calculate. The difference between the characteristic function obtained by machine learning and the traditional method is very small, but the calculation method is simpler and more universal. After that, we apply the method to the actual scene. By solving the molecular dynamics simulation of alanine dipeptide structure in polymer protein molecule, the characteristic function of dihedral angle folding of alanine dipeptide structure was preliminarily calculated. The results were consistent with the traditional method.