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Traditional approaches based on finite element analyses have beensuccessfully used to predict the macro-scale behavior of heterogeneousmaterials (composites, multicomponent alloys, and polycrystals) widely used inindustrial applications. However, this necessitates the mesh size to be smallerthan the characteristic length scale of the microstructural heterogeneities inthe material leading to computationally expensive and time-consumingcalculations. The recent advances in deep learning based image super-resolution(SR) algorithms open up a promising avenue to tackle this computationalchallenge by enabling researchers to enhance the spatio-temporal resolution ofdata obtained from coarse mesh simulations. However, technical challenges stillremain in developing a high-fidelity SR model for application to computationalsolid mechanics, especially for materials undergoing large deformation. Thiswork aims at developing a physics-informed deep learning based super-resolutionframework (PhySRNet) which enables reconstruction of high-resolutiondeformation fields (displacement and stress) from their low-resolutioncounterparts without requiring high-resolution labeled data. We design asynthetic case study to illustrate the effectiveness of the proposed frameworkand demonstrate that the super-resolved fields match the accuracy of anadvanced numerical solver running at 400 times the coarse mesh resolution whilesimultaneously satisfying the (highly nonlinear) governing laws. The approachopens the door to applying machine learning and traditional numericalapproaches in tandem to reduce computational complexity accelerate scientificdiscovery and engineering design.

PhySRNet: Physics informed super-resolution network for application in computational solid mechanics