Flow reconstruction from noisy sparse measurements with strictly-enforced convolutional neural networks*

We develop a physics-constrained dual-branch convolutional neural network to reconstruct turbulent flows from sparse measurements without access to the full flow fields. We investigate three loss functions: a PINN-like loss, the strictly enforced loss, and the strictly enforced mean loss, which we developed. The loss functions have different types of constraints on the measurements, where 'strict' means that the reconstructed flow at sensor locations is forced to match the measurement. First, we assume the measurements are non-noisy. We find that the strictly enforced loss, which places a strict constraint on the instantaneous measurements, can accurately reconstruct the flow. Second, we assume the measurements are corrupted with noise and design the strictly enforced mean loss, which places a strict constraint on the mean of the measurements. We find the strictly enforced mean loss recovers physical instantaneous snapshots even at high noise levels. The proposed method enables the reconstruction of turbulent flows from noisy, sparse measurements without access to the ground truth.