Session: 12-06-01: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials

Paper Number: 143855

143855 - Geom-Deeponet: A Point-Cloud-Based Deep Operator Network for Field Predictions on 3d Parameterized Geometries 

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. Since the designs are 3D in nature, repeated simulations of different design iterations might be computationally expensive. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide design insights. Nevertheless, few available NNs reported in the literature can handle solution prediction on varying 3D shapes. In this work, we present a novel deep operator network (DeepONet) variant called Geom-DeepONet, which encodes parameterized 3D geometries and predicts full-field solutions on an arbitrary number of nodes. To the best of the authors' knowledge, this is the first attempt in the literature and is our primary novelty. In addition to expressing shapes using mesh node coordinates, the signed distance function for each node is evaluated and used to augment the inputs to the trunk network of the Geom-DeepONet, thereby capturing both explicit and implicit representations of the 3D shapes. The powerful geometric encoding capability of a sinusoidal representation network (SIREN) is also exploited by replacing the classical feedforward neural networks in the trunk with SIREN. Additional data fusion between the branch and trunk networks is introduced by an element-wise product. A numerical benchmark was conducted to compare Geom-DeepONet to PointNet and vanilla DeepONet, two existing NN architectures in the literature capable of 3D full-field predictions. The numerical results show that our architecture trains extremely fast with a much smaller GPU memory footprint compared to PointNet. Among the three models, Geom-DeepONet yields the most accurate results, with less than 2 MPa stress error.  When testing the trained model on dissimilar designs, it is observed that our model shows a much lower generalization error than vanilla DeepONet. Once trained, the model can predict vector solutions, including all three displacement components and the von Mises stress. The prediction speed can be over 10^5 times faster than implicit finite element simulations for large meshes. The prediction time of our model scales as O(N^0.83), as compared to the time scaling of implicit finite element simulations O(N^1.36), showing significant computational efficiency. With the small memory footprint of the trained model, a single A100 GPU card with 40GB of memory can accommodate predictions on meshes with up to 70 million degrees of freedom. The ability of the proposed model to perform efficient and accurate field predictions on variable 3D geometries, especially those discretized by different nodes and elements, makes it a valuable tool for preliminary performance evaluation and design optimizations and is the most significant contribution of the current work.

Presenting Author: Junyan He Ansys Inc.

Presenting Author Biography: Junyan He obtained his Ph.D. in Mechanical Engineering from the University of Illinois at Urbana-Champaign in 2023. His research focuses on the combination and synergy of finite element simulations with scientific machine learning. He currently works as a senior application engineer at Ansys Inc.

Authors:

Junyan He Ansys Inc.
Seid Koric University of Illinois at Urbana-Champaign
Diab Abueidda University of Illinois at Urbana-Champaign
Ali Najafi Ansys Inc.
Iwona Jasiuk University of Illinois at Urbana-Champaign