A neural network optimization scheme for fractional economic and environmental mathematical model

The Economic and Environmental (EE) model plays a vital role in economic science by describing the interaction between economic growth and environmental factors. In this work, we propose a Physics-Informed Neural Network (PINN) method enhanced by the Theory of Functional Connections (TFC) to solve the EE system efficiently. TFC makes the neural network satisfy the initial conditions, which improves accuracy. Shifted Chebyshev polynomials are used as activation functions. The Subtraction and Average-Based Optimization (SABO) method is applied, and it compared with Particle Swarm Optimization (PSO). The Adams–Bashforth–Moulton (ABM) is used as a numerical method. Using supervised learning, the Levenberg-Marquardt neural network (LMNN) approach is employed. Error analysis and graphical comparisons, shows that the proposed SABO method achieves superior accuracy then the PSO and ABM methods.