Physics-Aware Flow Data Completion Using Neural Inpainting

Sebastien Foucher, Jingwei Tang, Vinicius da Costa de Azevedo, Byungsoo Kim, Markus Gross, Barbara Solenthaler

TL;DR: We present a network architecture and loss functions for inpainting fluid flow data that considers physical properties and constraints.

Abstract: In this paper we propose a physics-aware neural network for inpainting fluid flow data. We consider that flow field data inherently follows the solution of the Navier-Stokes equations and hence our network is designed to capture physical laws. We use a DenseBlock U-Net architecture combined with a stream function formulation to inpaint missing velocity data. Our loss functions represent the relevant physical quantities velocity, velocity Jacobian, vorticity and divergence. Obstacles are treated as known priors, and each layer of the network receives the relevant information through concatenation with the previous layer's output. Our results demonstrate the network's capability for physics-aware completion tasks, and the presented ablation studies show the effectiveness of each proposed component.

Keywords: neural inpainting, fluid dynamics, flow data completion, physics-aware network