Exploring the fractal exothermic reactions model with constant heat source and porous media via a novel fractal physics-informed neural networks method

In this work, a novel fractal physics-informed neural networks (PINNs) method is proposed to solve the fractal exothermic reactions model with constant heat source and porous media for the microgravity. On integrating the physical information of the considered equation into the neural networks with the aid of the two-scale transformation, we convert the numerical approximate solution problem into the optimization problems of boundaries and governing equation. The Adam algorithm is adopted to optimize the loss function through training process to obtain the predicted results. Two different examples are given to validate the robustness and efficiency of the fractal PINNs method. As anticipated, compared with the existing approximate solutions for the fractal order Formula: see text, a well agreement is reached, which reveals the validity and correctness of the proposed method. Furthermore, the predicted results of the different fractal orders are also presented. The findings in this work are expected to offer some new ideas for solving the fractal NPDEs in thermal science and engineering.