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

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.