MechSE-NCSA work demonstrates important step toward AI-driven modeling and design in complex engineering phenomena
A cutting-edge research collaboration at the intersection of artificial intelligence and classical numerical methods in computational mechanics has been featured as the additional cover of the January 2023 issue of the International Journal of Numerical Methods in Engineering.
The paper, “On the use of graph neural networks and shape-function-based gradient computation in the deep energy method,” is authored by mechanical engineering doctoral candidate Junyan (Jimmy) He; alumnus and NSCA research scientist Diab Abueidda (PhD ME ’20); MechSE Research Associate Professor and NCSA Technical Associate Director Seid Koric; and MechSE Professor Iwona Jasiuk.
The abstract states, “A graph convolutional network (GCN) is employed in the deep energy method (DEM) model to solve the momentum balance equation in three-dimensional space for the deformation of linear elastic and hyperelastic materials due to its ability to handle irregular domains over the traditional DEM method based on a multilayer perceptron (MLP) network. The method's accuracy and solution time are compared to the DEM model based on a MLP network. We demonstrate that the GCN-based model delivers similar accuracy while having a shorter run time through numerical examples. Two different spatial gradient computation techniques, one based on automatic differentiation (AD) and the other based on shape function (SF) gradients, are also accessed. We provide a simple example to demonstrate the strain localization instability associated with the AD-based gradient computation and show that the instability exists in more general cases by four numerical examples. The SF-based gradient computation is shown to be more robust and delivers an accurate solution even at severe deformations. Therefore, the combination of the GCN-based DEM model and SF-based gradient computation is potentially a promising candidate for solving problems involving severe material and geometric nonlinearities.”
“This article combines several novelties in our ongoing research on applying artificial intelligence (AI) methods to solve classical computational mechanics problems. We devised the artificial neural network of the graph convolutional type, which can better learn structural relations among the nodes discretizing the domain,” said He. “The network is ‘informed’ by the underlying physics we solve of a hyperelastic deformable body. Finally, the gradient calculations of the network’s loss with respect to the trainable parameters are performed by shape function gradients providing a more accurate and robust solution for irregular geometries with highly nonlinear material responses.”
The collaboration among MechSE and NCSA researchers was performed under the new Illinois Computes Program and performed on the cutting-edge GPU resource Delta at NCSA and is an essential step towards AI-driven modeling and design in many complex phenomena and processes in engineering and science.