Helicity-conservative Physics-informed Neural Network Model for Navier-Stokes Equations

TL;DR

This paper introduces a helicity-conservative physics-informed neural network model for Navier-Stokes equations that ensures helicity conservation, demonstrating its advantages over finite element methods through theoretical and numerical validation.

Contribution

The paper proposes a novel physics-informed neural network model that conserves helicity in Navier-Stokes equations using a strong form PDE-based loss function.

Findings

The strong form PDE-based PINN better preserves helicity than other methods.

Theoretical analysis confirms helicity conservation in the proposed model.

Numerical results support the effectiveness of the model in conservation tasks.

Abstract

We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce helicity conservation. Physics-informed neural network model is based on the strong form of PDE. We compare the proposed Physics-informed neural network model and a relevant helicity-conservative finite element method. We arrive at the conclusion that the strong form PDE is better suited for conservation issues. We also present theoretical justifications for helicity conservation as well as supporting numerical calculations.