Reconstruct the biomass particles fields in the particle-fluid problem using continuum methods by applying the physics-informed neural network

The motion of particles in the moving grate combustion chamber is used as the case study. These problems are categorized as particle-fluid problems. They are typically solved using Lagrangian-Eulerian methods, one of which is the coupling between the discrete element method (DEM, which is applied to the particles phase) and the computational fluid dynamics method (CFD, which is applied to the fluid phase). The current study's objective is to avoid coupling and instead, focusing on using the CFD method only. There are dense piles of particles moving on the grates in the biomass combustion chamber. We assumed the dense particles' behaviors similar to the fluid, and then, applied the fluid governing equations to the particles phase. The virtual fields of the velocities, pressure and density are specified for the particles' phase. Afterward, the physics-informed neural network (PINN) is used to reconstruct particles' fields and additionally to investigate the capability of the predicted fields to satisfy the fluid governing equations. This model has the benefit of reconstructing the particles' fields without the need for boundaries and initial conditions. The precision of the model is assessed by comparing the test data set with the exact data obtained from the eXtended discrete element method (XDEM is an in-house software). It is demonstrated that the trained neural network delivered high accuracy and is capable of predicting all outputs with an error value of less than 2 percent. Additionally, to choose the optimum architecture for the neural network, the effect of the number of hidden layers and neurons is studied.