Traditional approaches based on finite element analyses have been successfully used to predict the macro-scale behavior of heterogeneous materials (composites, multicomponent alloys, and polycrystals) widely used in industrial applications. However, this necessitates the mesh size to be smaller than the characteristic length scale of the microstructural heterogeneities in the material leading to computationally expensive and time-consuming calculations. The recent advances in deep learning based image super-resolution (SR) algorithms open up a promising avenue to tackle this computational challenge by enabling researchers to enhance the spatio-temporal resolution of data obtained from coarse mesh simulations. However, technical challenges still remain in developing a high-fidelity SR model for application to computational solid mechanics, especially for materials undergoing large deformation. This work aims at developing a physics-informed deep learning based super-resolution framework (PhySRNet) which enables reconstruction of high-resolution deformation fields (displacement and stress) from their low-resolution counterparts without requiring high-resolution labeled data. We design a synthetic case study to illustrate the effectiveness of the proposed framework and demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution while simultaneously satisfying the (highly nonlinear) governing laws. The approach opens the door to applying machine learning and traditional numerical approaches in tandem to reduce computational complexity accelerate scientific discovery and engineering design.
翻译:以有限要素分析为基础的传统方法已被成功地用于预测工业应用中广泛使用的多种材料(复合材料、多成分合金和多元晶体)的宏观行为。然而,这要求网形尺寸必须小于导致计算成本昂贵和耗时计算的材料中微结构异质的典型长度尺度。最近深学习基于图像超分辨率(SR)算法的进展为应对这一计算挑战开辟了一条有希望的途径,使研究人员能够加强从粗微中模拟获得的数据的瞬时分辨率。然而,在为计算固态机械,特别是正在发生大规模畸形的材料开发高不灵敏性SR模型方面,技术挑战依然存在。这项工作旨在开发一个基于物理的深层次学习的超分辨率框架(PhySRNet),以便能够在不需要高分辨率标签数据的情况下重建低分辨率变形场(变形和压力),从而解决这一计算挑战。我们设计了一个综合案例研究,用以说明在不要求高分辨率模拟中获取的数据的瞬时,在开发高灵敏性SR模型模型模型模型模型时,特别是在进行计算固化的精确度设计方法的同时,同时,在进行高清晰度的精确度的精确度的精确度的精确度计算方法中,以显示数字解析的精确度的精确度研究。