CMML members Jie and Enjamamul presented talks at the 2021 Engineering Mechanics Institute Conference:
Minisymposium #213 Machine Learning-based Computational Modeling for Civil Engineering Applications
#2032317 Data-Driven Modeling of Multi-Parameter Mechanical Problems in Heterogeneous Media
Authors: Jie Hou, Jun Li, Alfa Heryudono
Predicting full-field responses of multi-parameter mechanical problems in heterogeneous material systems is of fundamental importance and has a variety of applications in design optimizations, uncertainty quantification, and structural health monitoring. Physics-based simulations such as the finite element method (FEM) provide high-fidelity predictions but can be computationally expensive and challenging in scenarios of real-time interactive design evaluations and decision-making. On the other hand, data-driven approaches encoded with physical constraints have the promise to rapidly predict reliable results for real-time application scenarios. In this study, a sequence of numerical examples with multi-dimensional parameters of heterogeneous material distributions is considered. Model order reduction techniques of proper orthogonal decomposition (POD) and proper generalized decomposition (PGD) are utilized to reduce the high-dimensional field response variables, respectively. POD is a posteriori method based on the snapshot matrix of field results, while PGD builds on a priori separated representation of the objective field to counter the curse of dimensionality. In POD based framework, an artificial neural network was employed to predict field responses based on POD reduced modes. In PGD based framework, the field responses are approximated by PGD reduced modes in a separated form with extra-coordinates of material variations. Both approaches are capable to predict full-field responses with satisfactory accuracy at a lower computational cost.
Minisymposium #255 Physics Informed Machine Learning for Data-driven Modeling and Discovery of Complex Systems
#2032312: Deep-Learning based Stress-Field Prediction of Heterogeneous Media
Authors: Enjamamul Hoq, Osama Aljarrah, Jun Li, Alfa Heryudono, Jing Bi
Rapid and accurate stress-field prediction in heterogeneous material systems is critical for a variety of applications, including design optimization, uncertainty quantification, structural monitoring, and predictive maintenance. The purpose of this research was to design and evaluate several deep learning-based frameworks for capturing the high-dimensional stress field responses of heterogeneous media. The first framework employs a combination of model order reduction and artificial neural networks (ANN). Using correct orthogonal decomposition, the stress fields are first projected to a low-dimensional representation (POD). Following that, ANN is used to restore the dimensionality of the minimized predicted fields. The second framework is based on a deep Convolutional Neural Network (CNN), while the third framework is based on a conditional Generative Adversarial Network (GAN) (cGAN). Two numerical examples were analyzed to determine the efficacy of the suggested frameworks. The first is a panel containing a variety of heterogeneous material inclusions that vary in terms of position and size. In the second example, a plate with holes of varied positions and sizes is considered. Both CNN and cGAN models accurately caught stress concentrations and whole stress fields. The suggested frameworks based on deep learning shown remarkable potential for modeling whole stress fields for a variety of heterogeneous materials.