Enhancement of physics-informed neural networks in applications to fluid dynamics

In this work, a novel deep learning algorithm is proposed within the framework of the physics-informed neural network (PINN) architecture. Physical constraints are incorporated through the Navier–Stokes and continuity equations, which are commonly used in fluid mechanics applications. The proposed approach addresses the challenge posed by the multicomponent nature of the PINN's loss function. This challenge arises from the need to determine an optimal weight configuration for the various components of the loss function. The issue is resolved by dynamically updating the weight configuration to balance the influence of different data types during training. The procedure, known as GradNorm, originally developed for deep multitask networks in computer vision, is adapted and integrated into the PINN framework. GradNorm adjusts the weight configuration to equalize the gradients of the loss function components. The new algorithm achieves a 50% improvement in accuracy compared to the conventional PINN in reconstructing the back-facing step flow. For the Taylor–Couette flow (Taylor vortex mode) test case, where the conventional PINN fails to capture the flow structure, the proposed approach demonstrates high accuracy even with sparse training datasets. Additionally, it does not require known flow parameter values in close proximity to walls to achieve accurate near-wall resolution. The application of the new algorithm shows great potential for processing sparse experimental datasets to reconstruct detailed flow fields and for providing a continuous representation of discrete solutions.