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

In this paper, we introduce an improved water strider algorithm designed to solve the inverse form of the Burgers-Huxley equation, a nonlinear partial differential equation. Additionally, we propose a physics-informed neural network to address the same inverse problem. To demonstrate the effectiveness of the new algorithm and conduct a comparative analysis, we compare the results obtained using the improved water strider algorithm against those derived from the original water strider algorithm, a genetic algorithm, and a physics-informed neural network with three hidden layers. Solving the inverse form of nonlinear partial differential equations is crucial in many scientific and engineering applications, as it allows us to infer unknown parameters or initial conditions from observed data. This process is often challenging due to the complexity and nonlinearity of the equations involved. Meta-heuristic algorithms and neural networks have proven to be effective tools in addressing these challenges. The numerical results affirm the efficiency of our proposed method in solving the inverse form of the Burgers-Huxley equation. The best results were obtained using the improved water strider algorithm and the physics-informed neural network with 10,000 iterations. With this iteration count, the mean absolute error of these algorithms is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup><mml:mn>10</mml:mn> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>4</mml:mn></mml:mrow> </mml:msup> <mml:mo>)</mml:mo></mml:mrow> </mml:math> . Additionally, the improved water strider algorithm is nearly four times faster than the physics-informed neural network. All algorithms were executed on a computing system equipped with an Intel(R) Core(TM) i7-7500U processor and 12.00 GB of RAM, and were implemented in MATLAB.