Abstract
Predicting full-field responses from multi-parametric mechanical problems in heterogeneous material systems is of fundamental importance. It has a variety of applications in design optimizations, uncertainty quantification, and structural health monitoring. Physics-based simulations such as the finite element method provide high-fidelity predictions. However, they 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 predict reliable results for real-time application scenarios rapidly. This study considers a sequence of numerical examples with multi-dimensional parameters of heterogeneous material distributions. 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 an a posteriori method based on the snapshot matrix of field results, while PGD builds on an a priori separated representation of the objective field to counter the curse of dimensionality. In POD based framework, Machine learning methods and artificial neural networks were 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 of mode functions with extra coordinates of material variations. Both approaches are capable of predicting physics field responses with satisfactory accuracy at a lower computational cost.