Research on the Data-Driven Differential Equation-Solving Algorithm Based on Artificial Intelligence

Abstract

Data-driven DEs has gained popularity in the past few years. This work proposes the new framework, named Adam Gannet Optimization Algorithm (AdamGOA), that combines Adam Optimization and Gannet Optimization Algorithm (GOA) to improve a stability, solve higher order Differential Equations (DE) and accuracy of DE. Adam is a first-order gradient-based methods, optimizes stochastic objectives using adaptive lower-order moments. In contrast, GOA represents a different distinct action of a gannets mathematically during foraging and is employed to facilitate exploitation and exploration. In addition, a Shepard Convolutional Neural Network (ShCNN) processed data to construct meta-data and estimate derivatives. After that, the unified integral form is established to determine optimal structure. Heterogeneous parameters are used to estimate and are labeled as constants or variables. Furthermore, the experimental findings showed that the AdamGOA_ ShCNN beat leading models in Accuracy, Convergence, and Mean Square Error (MSE), with values of 0.989, 4, and 0.539, respectively.