Fast modeling and understanding fluid dynamics systems with encoder–decoder networks

Is a deep learning model capable of representing systems governed by certain first principle physics laws by only observing the system's output? In an effort to simulate two-dimensional subsurface fluid dynamics in porous media, we found that an accurate deep-learning-based proxy model can be taught efficiently by a computationally expensive finite-volume-based simulator. We pose the problem as an image-to-image regression, running the simulator with different input parameters to furnish a synthetic training dataset upon which we fit the deep learning models. Since the data is spatiotemporal, we compare the performance of three alternative treatments of time; a convolutional LSTM, an autoencoder network that treats time as a direct input and an echo state network. Adversarial methods are adopted to address the sharp spatial gradient in the fluid dynamics problem. Compared to traditional simulation, the proposed deep learning approach enables much faster forward computation, which allows us to explore more scenarios with a much larger parameter space given the same time. It is shown that the improved forward computation efficiency is particularly valuable in solving inversion problems, where the physics model has unknown parameters to be determined by history matching. By computing the pixel-level attention of the trained model, we quantify the sensitivity of the deep learning model to key physical parameters and hence demonstrate that the inverse problem can be solved with great acceleration. We assess the efficacy of the machine learning surrogate in terms of its training speed and accuracy. The network can be trained within minutes using limited training data and achieve accuracy that scales desirably with the amount of training data supplied.