Abstract
Data science is a multidisciplinary field that plays a crucial role in extracting valuable insights and knowledge from large and intricate datasets. It has the potential to drive accurate predictions and enhance decision-making capabilities across various domains, including finance, marketing, healthcare, and scientific disciplines. In this paper, we developed a multiscale entropy dynamic (MED) methodology that is applicable to the field of data science. As an example, we apply this methodology to the data science framework of a large and intricate quantum mechanical system composed of particles. Our research demonstrates that the dynamic and probabilistic nature of such systems can be effectively addressed using the proposed MED approach. Through this approach, we are able to describe the system's dynamics in a multiscale form of equation of motion which turned out to be a general form of the Nonlinear Schrödinger Equation (NSE). It becomes the conventional linear Schrödinger equation for the case of smallest size particles, namely electrons, and quite expectedly nonlinear Schrödinger equation for the cases of quasi-particles, such as plasmons, polarons, and solitons. By employing this innovative approach, we pave the way for a deeper understanding of quantum mechanical systems and their behaviors within complex materials.