Physics-Constrained Generative Adversarial Networks for 3D Turbulence
This work addresses the need for reliable physics-constrained models in fluid dynamics simulations, representing an incremental improvement over existing penalty-based methods.
The paper tackled the problem of enforcing physics constraints in generative models for 3D turbulence by developing hard constraints embedded in GANs, specifically to enforce mass conservation, and demonstrated its feasibility through physics-informed diagnostics.
Generative Adversarial Networks (GANs) have received wide acclaim among the machine learning (ML) community for their ability to generate realistic 2D images. ML is being applied more often to complex problems beyond those of computer vision. However, current frameworks often serve as black boxes and lack physics embeddings, leading to poor ability in enforcing constraints and unreliable models. In this work, we develop physics embeddings that can be stringently imposed, referred to as hard constraints, in the neural network architecture. We demonstrate their capability for 3D turbulence by embedding them in GANs, particularly to enforce the mass conservation constraint in incompressible fluid turbulence. In doing so, we also explore and contrast the effects of other methods of imposing physics constraints within the GANs framework, especially penalty-based physics constraints popular in literature. By using physics-informed diagnostics and statistics, we evaluate the strengths and weaknesses of our approach and demonstrate its feasibility.