Weakly-supervised Deep Learning Model for Fast Approximations of Fluid Dynamics

Many deep-learning-based problems depend on a significant amount and high quality of the dataset, while in the “small data” regime, less work and related applications have been established. The computational cost of fluid dynamics simulations limits the scale, predictability, and use in physics-conforming control systems for mobile and low-powered devices. Some state-of-the-art works have shown the possibility to solve deep-learning-based simulation problems with labeled training data. Here, a physics-informed model is established without the need for computationally expensive simulation results by a stacked U-Net architecture trained in a weakly-supervised manner on computationally-efficient low-dimensional simulations. To enforce physical laws, a custom physics informed loss is developed which when trained progressively allows the model to approximate the N-S with various obstacles, boundary conditions, and mesh density with high fidelity. The model approximates computational simulations that take many CPU minutes with a machine learning model that can achieve millisecond-level inference on a consumer-grade computer. This work provides an extensible methodology for fast, large-scale computational simulations and real-time on-edge computational simulations that would normally require distributed parallel computing. This result represents a discovery in accelerating important and complex fluid dynamics simulations.