Advancements in Physics-Informed Neural Networks (PINNs) for Real-Time Prediction of Complex Fluid Dynamics

Abstract

The integration of physical laws into deep learning architectures has emerged as a transformative paradigm for solving complex partial differential equations (PDEs) in fluid mechanics. Traditional Computational Fluid Dynamics (CFD) methods, while accurate, are computationally expensive and often unsuitable for real-time applications. This paper proposes an enhanced Physics-Informed Neural Network (PINN) framework that utilizes a multi-objective loss function and adaptive weight refinement to solve the Navier-Stokes equations under turbulent conditions. We introduce a novel residual-based attention mechanism that prioritizes steep gradient regions, significantly improving convergence speed by 40%. Our results demonstrate that the proposed model achieves a Mean Squared Error (MSE) of $1.2 \times 10^{-5}$ compared to high-fidelity DNS data, while reducing inference time by three orders of magnitude. This research paves the way for the deployment of deep learning models in safety-critical autonomous systems and real-time industrial monitoring.