An improved water strider algorithm for solving the inverse Burgers Huxley equation

Area of Science:

• Computational Mathematics
• Applied Mathematics
• Numerical Analysis

Background:

• Nonlinear partial differential equations (PDEs) like the Burgers-Huxley equation are vital in modeling complex phenomena.
• Solving the inverse form of these PDEs is critical for parameter inference from observational data.
• Challenges arise from the inherent nonlinearity and complexity of these equations.

Purpose of the Study:

• To introduce an improved water strider algorithm for the inverse Burgers-Huxley equation.
• To propose a physics-informed neural network (PINN) for the same inverse problem.
• To compare the performance of the improved water strider algorithm against existing methods, including the original water strider algorithm, a genetic algorithm, and a standard PINN.

Main Methods:

• Development of an enhanced water strider algorithm.
• Implementation of a physics-informed neural network (PINN).
• Comparative numerical analysis using MATLAB on a standardized hardware configuration.

Main Results:

• Both the improved water strider algorithm and the PINN achieved high accuracy in solving the inverse Burgers-Huxley equation with 10,000 iterations.
• The improved water strider algorithm demonstrated a significant speed improvement, being nearly four times faster than the PINN.
• The mean absolute error for both top-performing methods was $$ at 10,000 iterations.

Conclusions:

• The improved water strider algorithm is a highly efficient and accurate method for solving the inverse Burgers-Huxley equation.
• Physics-informed neural networks offer a viable alternative for this inverse problem.
• The enhanced water strider algorithm presents a computationally advantageous approach, particularly when speed is a critical factor.