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In a finite element analysis, using a large number of grids is important toobtain accurate results, but is a resource-consuming task. Aiming to real-timesimulation and optimization, it is desired to obtain fine grid analysis resultswithin a limited resource. This paper proposes a super-resolution method thatpredicts a stress tensor field in a high-resolution from low-resolution contourplots by utilizing a U-Net-based neural network which is called PI-UNet. Inaddition, the proposed model minimizes the residual of the equilibriumconstraints so that it outputs a physically reasonable solution. The proposednetwork is trained with FEM results of simple shapes, and is validated with acomplicated realistic shape to evaluate generalization capability. AlthoughESRGAN is a standard model for image super-resolution, the proposed U-Net basedmodel outperforms ESRGAN model in the stress tensor prediction task.

Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net