Distributed physics informed neural network for data-efficient solution to partial differential equations
This work addresses the challenge of solving complex PDEs like Navier-Stokes more efficiently for computational physics and engineering applications, though it is incremental as it builds on existing PINN methods.
The authors tackled the limited representation capability of physics informed neural networks (PINNs) for solving partial differential equations (PDEs) by proposing a distributed PINN (DPINN), which achieved more accurate and data-efficient solutions, such as solving the Navier-Stokes equation for the first time with this method.
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial differential equations (PDEs). However, the literature lacks detailed investigation of PINNs in terms of their representation capability. In this work, we first test the original PINN method in terms of its capability to represent a complicated function. Further, to address the shortcomings of the PINN architecture, we propose a novel distributed PINN, named DPINN. We first perform a direct comparison of the proposed DPINN approach against PINN to solve a non-linear PDE (Burgers' equation). We show that DPINN not only yields a more accurate solution to the Burgers' equation, but it is found to be more data-efficient as well. At last, we employ our novel DPINN to two-dimensional steady-state Navier-Stokes equation, which is a system of non-linear PDEs. To the best of the authors' knowledge, this is the first such attempt to directly solve the Navier-Stokes equation using a physics informed neural network.