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

Numerical methods such as Finite element method [Hug12], Isogeomteric analysis [CHB09], and mesh-free methods [LJZ95, BLG94] are few of the conventional approaches employed in solving the Partial Differential Equations (PDEs) involved in computational solid mechanics problems. However, the ever-increasing sophistication of material models by incorporating more complex physics, such as modeling size-effect [FMAH94, AA20b] or dislocation density evolution [AZA20, Aro19, AA20a, AAA22, JABG20], or advanced materials such as composites and multicomponent alloys with spatially-varying material properties (heterogeneity) and direction dependent behavior (anisotropy) is bringing these numerical solvers to their limits. Hence, it is becoming a formidable task to perform simulations that can resolve the complex physical phenomena occurring at small spatial and temporal scales and accurately predict the macro-scale behavior of materials. Therefore, a cost-effective physicsbased surrogate model that allows the researchers to perform simulations on a coarse mesh without sacrificing accuracy will be highly beneficial for many reasons. First, researchers can choose to run their simulations at a lower resolution (online stage) and later reconstruct the solution back to the target resolution (offline stage). This will significantly reduce the computational expense during the online stage, thus accelerating the process of scientific investigation and discovery. Second, the surrogate model based on data super-resolution can also be used to enhance outputs from experimental techniques for full-field displacement and strain measurement such as Digital Image Correlation (DIC) which would allow researchers to generate and store a small fraction of data. Recent advances in Deep Learning (DL) and Physics-Informed Neural Networks (PINN) [RPK17, RPK19] make it a promising tool to tackle this computational challenge.