2024/05/22 by Hamidreza Eivazi, Mahyar Alikhani, Eivazi, Hamidreza +9
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Computational Engineering #FOS: Computer and information sciences #Finance #Machine Learning (cs.LG) #Model Reduction and Neural Networks #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2405.13759
openalex publication_date 2024/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the demand of solving initial boundary-value problems at multiple scales. On the other hand, multiscale finite element computations are commended for their ability to integrate micro-structural properties into macroscopic computational analyses using homogenization techniques. Recently, neural operator-based surrogate models have shown trustworthy performance for solving a wide range of partial differential equations. In this work, we propose a hybrid method in which we utilize deep operator networks for surrogate modeling of the microscale physics. This allows us to embed the constitutive relations of the microscale into the model architecture and to predict microscale strains and stresses based on the prescribed macroscale strain inputs. Furthermore, numerical homogenization is carried out to obtain the macroscale quantities of interest. We apply the proposed approach to quasi-static problems of solid mechanics. The results demonstrate that our constitutive relations-aware DeepONet can yield accurate solutions even when being confronted with a restricted dataset during model development.