SnapPINN: Pressure and Energy Dissipation Reconstruction from a Sparse and Noisy Velocity Snapshot

Abstract

Reconstructing pressure and turbulence quantities from experimental velocity measurements is challenging, especially without time-resolved data. Furthermore, limitations such as low seeding density, finite resolution, and measurement noise severely hinder the reconstruction of accurate flow fields. We introduce SnapPINN, a two-stage physics-informed neural network (PINN) that successfully reconstructs 3D velocity, their spatial gradients, pressure fields and estimates turbulent kinetic energy dissipation from a single snapshot of sparse, noisy velocity data. Evaluated here on 3D DNS turbulent pipe flow data, SnapPINN uses a sine-activated architecture with sequentially trained, decoupled velocity and pressure sub-networks. In stage 1, the velocity network fits particle data while enforcing incompressibility, serving as a physically consistent smoothing operator that regularises velocity gradients against noise. In stage 2, the velocity network is frozen, and the pressure network is trained using the pressure Poisson equation and the pretrained velocity gradients. We systematically map reconstruction performance of SnapPINN across 100 test cases to mimic challenging experimental, such as adding significant position noise, linearization of velocity field and seeding sparsity as low as $0.07\%$ of the fully resolved DNS grid. Quantitatively, bulk velocity was reconstructed within $0.5\%$, while errors remained below $50\%$ for the gradient-sensitive energy dissipation rate and within $4$--$24\%$ for the a~posteriori inferred $\mathrm{Re}_τ$, even under extremely sparse and noisy conditions. Finally, we establish a practical reliability map that shows which experimental conditions are likely to yield reliable SnapPINN reconstructions in the absence of ground truth.