Flow field reconstruction from sparse and noisy data based on finite volume physics-informed neural networks

2026/03/01 by Zhiyuan Geng, Hailong Liu, Rui Deng +3
Computer Science · Physics and Astronomy · #Generative Adversarial Networks and Image Synthesis #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing

paper · doi:10.1063/5.0307754

openalex publication_date 2026/03/01 · openalex created_date 2026/03/18 · openalex updated_date 2026/07/31

Abstract

Flow field reconstruction from sparse and noisy data remains a challenging task in fluid mechanics due to low efficiency and high hardware demands. This study introduces the finite volume method into the physics-informed neural network (PINN) method, proposing a finite volume physics-informed neural network (FVPINN) method under weak-form constraints. The method transforms volume integrals to surface integrals via the divergence theorem and employs control volume discretization, thereby reducing reliance on automatic differentiation for high-order derivatives. The experimental results show that FVPINNs achieve comparable prediction accuracy to Vanilla PINNs in the two-dimensional (2D) steady Cavity flow and Kovasznay flow problems, under both noiseless and noisy conditions, with average training time reduced by 44.91% and 43.94%, respectively. In the unsteady 2D cylinder flow scenarios, FVPINNs exhibit slightly higher sensitivity to noise, particularly in velocity field reconstruction, yet still maintain predictive performance comparable to Vanilla PINNs across all noise levels. Notably, FVPINNs achieve a significant reduction of 45.46% in average training time, highlighting their superior computational efficiency in transient flow modeling. Overall, FVPINNs significantly improve computational efficiency while maintaining prediction accuracy, showing strong robustness and potential for broader application.

Citations

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
• NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• Multi-fidelity Bayesian neural networks: Algorithms and applications
• Physics-Informed Neural Networks for Heat Transfer Problems
• Applications of Physics-Informed Neural Networks in Power Systems - A Review
• Physics-informed neural networks (PINNs) for fluid mechanics: a review
• wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws

Related

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• Physics-Informed Neural Network Approaches for Sparse Data Flow Reconstruction of Unsteady Flow Around Complex Geometries
• Physics-informed deep-learning applications to experimental fluid mechanics
• Physics-informed neural networks (PINNs) for fluid mechanics: A review
• On the Preprocessing of Physics-informed Neural Networks: How to Better Utilize Data in Fluid Mechanics