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Soft biological tissues often have complex mechanical properties due tovariation in structural components. In this paper, we develop a novelUNet-based neural network model for inversion in elasticity (El-UNet) to inferthe spatial distributions of mechanical parameters from strain maps as inputimages, normal stress boundary conditions, and domain physics information. Weshow superior performance, both in terms of accuracy and computational cost, byEl-UNet compared to fully-connected physics-informed neural networks inestimating unknown parameters and stress distributions for isotropic linearelasticity. We characterize different variations of El-UNet and propose aself-adaptive spatial loss weighting approach. To validate our inversionmodels, we performed various finite-element simulations of isotropic domainswith heterogenous distributions of material parameters to generate syntheticdata. El-UNet is faster and more accurate than the fully-connectedphysics-informed implementation in resolving the distribution of unknownfields. Among the tested models, the self-adaptive spatially weighted modelshad the most accurate reconstructions in equal computation times. The learnedspatial weighting distribution visibly corresponded to regions that theunweighted models were resolving inaccurately. Our work demonstrates acomputationally efficient inversion algorithm for elasticity imaging usingconvolutional neural networks and presents a potential fast framework forthree-dimensional inverse elasticity problems that have proven unachievablethrough previously proposed methods.

Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials