PLEM-MHD: Physics-constrained Latent Evolution Model for Magnetohydrodynamics

The study of the flow behavior of electrically conducting fluids under electromagnetic fields finds applications across a wide range of physical systems. However, surrogate modeling of magnetohydrodynamics (MHD) presents significant challenges due to the non-linear, coupled, multi-scale spatial and temporal dynamics of the interacting fields. In this work, we proposed a latent evolution model where spatial features are learned in a lower dimensional latent representation followed by learning the temporal dynamics in the latent space. The methodology is computationally efficient, enables interpretability and flexible enough to incorporate physics-based objective functions as soft-constraints. We apply the physics-constrained latent evolution model (PLEM) to predict downstream MHD fields such as density, velocity, pressure, and magnetic fields using upstream measurements. The model demonstrates the ability to accurately reconstruct flow fields and forecast complex spatiotemporal dynamics with high fidelity.