Mathematical models for fluid flow in porous media with machine learning techniques for landfill waste leachate

In this article, we take a look at an Ordinary Differential Equation model that describes the bacteria’s role in anaerobic biodegradation dynamics of domestic garbage in a landfill. A nonlinear Ordinary Differential Equation system is used to describe biological activities. In the current study, the Levenberg–Marquardt Backpropagation Neural Network is used to locate alternate solutions for the model. The Runge–Kutta order four (RK-4) method is employed to produce reference solutions. Different scenarios were looked at to analyse our surrogate solution models. The reliability to verify the equilibrium of the mathematical model, physical quantities such as the half-saturation constant ( \(K_S\) $K_S$ ), the maximum growth rate ( \(\mu _m\) ${\mu }_m$ ), and the inhibition constant ( \(K_I\) $K_I$ ), can be modified. We categorise our potential solutions into training, validation and testing groups in order to assess how well our machine learning strategy works. The advantages of the Levenberg-Marquardt Backpropagation Neural Network scheme have been shown by studies that compare statistical data based on Mean Square Error Function, efficacy, regression plots, and error histograms. From the whole process we conclude that Levenberg–Marquardt Backpropagation Neural Network is accurate and authentic.