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Generative Adversarial Networks (GANs) have received wide acclaim among themachine learning (ML) community for their ability to generate realistic 2Dimages. ML is being applied more often to complex problems beyond those ofcomputer vision. However, current frameworks often serve as black boxes andlack physics embeddings, leading to poor ability in enforcing constraints andunreliable models. In this work, we develop physics embeddings that can bestringently imposed, referred to as hard constraints, in the neural networkarchitecture. We demonstrate their capability for 3D turbulence by embeddingthem in GANs, particularly to enforce the mass conservation constraint inincompressible fluid turbulence. In doing so, we also explore and contrast theeffects of other methods of imposing physics constraints within the GANsframework, especially penalty-based physics constraints popular in literature.By using physics-informed diagnostics and statistics, we evaluate the strengthsand weaknesses of our approach and demonstrate its feasibility.

Physics-Constrained Generative Adversarial Networks for 3D Turbulence