Data-Driven Parameter Discovery of a One-Dimensional Burgers' Equation Using a Physics-Informed Neural Network

Abstract. This work demonstrates the use of a Physics-Informed Neural Network (PINN) trained to solve supervised learning tasks respecting the law of physics described by the one-dimensional Burgers partial differential equation (PDE), and focuses on the problem of data-driven PDE parameter discovery. The Burgers' equation is one PDE with derivatives in space and time that is commonly solved by a numerical method. However, recent work proposes the use of PINN to solve, as a new class of data-efficient universal function approximators, which naturally encode any underlying physical laws as prior information. As the number of sample points required for efficient Deep Natural Network (DNN) training would be very high, PINN was proposed, allowing the use of a smaller number of sample points, and incorporating the related physical equation in the simulation. This work evaluates the discovery of parameters of the Burgers' equation through the use of PINN, for different hyperparameters and dataset sizes, seeking the best adjustment. The relative errors and processing times obtained are presented, running on the LNCC's Santos Dumont supercomputer.