Modeling the Burning of Polymer Matrix: Training Collocation Physics-Informed Neural Network

Abstract

Abstract The combined impacts of thermal, chemical, and physical processes play a significant role in the pyrolysis problems in polymeric materials. Thermal energy is transported into the material via thermal convection when the charring materials are subjected to high-temperature loading. Decomposition of the resin will result in pyrolytic gases and solid leftovers. The material can be split into three zones based on the degree of pyrolysis of the material: (i) charring zone, in which the material entirely decomposes; (ii) pyrolysis zone, in which the material is disintegrating; and (iii) virgin material zone, in which the material has not yet begun to decompose. Physics-informed neural networks (PINNs) are neural networks whose components contain model equations, such as partial differential equations (PDEs). A multi-task learning approach has emerged in which a NN must fit observed data while decreasing a PDE residual. This article introduces PINN architectures to forecast temperature distributions and the degree of burning of a pyrolysis problem in a one-dimensional (1D) and two-dimensional (2D) rectangular domain. The complex, non-convex multi-objective loss function presents substantial obstacles for forward problems in training PINNs. We discovered that adding several differential relations to the loss function causes an unstable optimization issue, which may lead to convergence to the trivial null solution or significant deviation of the solution. To address this problem, the dimensionless form of the coupled governing equations that we find most beneficial to the optimizer is used. The numerical results are compared with results obtained from PINN to show the performance of the solution. Our research is the first to explore fully coupled temperature-degree-of-burning relationships in pyrolysis problems. Unlike classical numerical methods, the proposed PINN does not depend on domain discretization. In addition to these characteristics, the proposed PINN achieves good accuracy in predicting solution variables, which makes it a candidate to be utilized for surrogate modeling of pyrolysis problems. In summary, the pyrolysis model of materials is solved with the PINN framework; We assumed that all thermal properties of a material (thermal conductivity, specific heat, and density) are affected by temperature and degree of burning. While the achieved results are close to our expectations, it should be noted that training PINNs is time-consuming. We relate the training challenge to the multi-objective optimization issue and the application of a first-order optimization algorithm, as reported by others. Given the difficulties encountered and overcome in this work for the forward problem, the next step is to use PINNs to inverse burning situations.