Optimal temperature trajectory for tubular reactor using physics informed neural networks

Abstract

Numerical approaches to solve partial differential equations (PDEs) governing the physical systems are very time consuming, and it limits their applications in online decision making. These physical systems can be modeled using a Neural network, and a nonlinear mapping can be obtained by capturing the knowledge represented by the PDEs governing the physical system. Such a Physics Informed Neural Network (PINN) generates a solution in a closed analytical form that maps the inputs of the PDE to its solution. In this paper, we exploit the advantage of obtaining this closed analytical form of solution for substantially easing the step of inverting such models for optimization. We demonstrate this capability by obtaining the optimal spatial temperature trajectory of a representative tubular reactor model to maximize the reactor yields. The PINN model was seen to accurately capture the dynamics of the tubular reactor governed by second order PDEs with spatial variables and temperature parameters as inputs. The results of modeling and optimization were compared with the finite difference method (FDM) of solving PDEs and were found to be computationally superior to the latter. The computational time taken by the PINN framework to obtain the optimal trajectory was significantly less than the traditional FDM method without compromising accuracy. Such approaches can supersede traditional methods where the governing physical models are computationally expensive and facilitate online decision making through the use of PINNs.