Finding The Governing Differential Equations In Free Form Through Data Analysis

Abstract

This paper proposes a methodology for the identification of governing differential equations based on empirical data. This method does not require any a priori specification of the equation's constituent pieces to be carried out in order to be successful. Because of this, there is no requirement for a pre-determined specification of the components that are to be included. The strategy that has been suggested has as its primary objective the simplification of the incorporation of a dataset or a set of datasets that are relevant to a particular solution or a group of particular solutions of a differential equation. The problem-solving approach that has been suggested is developed with the purpose of being flexible enough to adapt to either scenario. The end result is a differential equation that has been written down in a way that is simple enough for folks to comprehend. The equation has been changed and tweaked in order to provide a more accurate representation of the particular solutions that have been presented. Improving one's understanding of differentiable data models is the primary objective of this research project. In the following step, the outputs that are produced by these models are then utilized as inputs inside the framework of genetic programming. This approach makes use of graphical representations to explain calculations by employing a wide variety of functions, parameters, and sometimes differential operators that are applied to functions. Our method, which makes use of recursive applications of automatic differentiation, has the capacity to investigate any arbitrary combination of operators without needing any input from the user. This is made possible by the fact that it employs automatic differentiation. This method makes it easier to simplify the design and evaluation of differential operators. It also makes the process more efficient. In addition, we describe a methodology for participating in active learning with the purpose of identifying and addressing flaws within the suggested governing equations. Our ultimate goal is to improve the system. The implementation of this measure was done so in order to improve the accuracy of the results.