Robust estimation of pressure and velocity gradients from one time step in turbulent pipe flows via two-stage physics-informed neural networks

Kurzfassung

Physics-informed neural networks (PINNs) have emerged as a promising approach in fluid mechanics for reconstructing unknown flow quantities—such as pressure and temperature—from sparse velocity measurements by embedding the governing equations of fluid flow into the training process [1,2]. Although PINNs are well suited to handling spatially sparse data [3], they are typically trained using large datasets across multiple time steps, which makes them computationally expensive. Here, we propose a novel PINN framework that reconstructs pressure fields and energy dissipation rates in non-thermal turbulent flows using only a single time step of sparsely sampled three-dimensional velocity data involving training with the pressure Poisson equation, ∇^2 p=-(∂u_i)/(∂x_j ) 〖∂u〗_j/(∂x_i ), As input, we employ synthetic particle data generated by a direct numerical simulation (DNS) of turbulent pipe flow at a friction Reynolds number Reτ=180 with varying inter-particle spacings. While DNS data are used at this stage, the ultimate objective is to apply the framework to experimental particle data obtained from fast two-pulse measurement systems [4]. To evaluate the method under realistic conditions, we added simulated measurement noise to the data. The proposed PINN effectively corrects the velocity field, yielding over 90% accuracy in both pressure reconstruction and energy dissipation estimation. These results highlight the framework's strong potential for processing realistic, noisy experimental data.