Point-DeepONet: A Deep Operator Network Integrating PointNet for Nonlinear Analysis of Non-Parametric 3D Geometries and Load Conditions
This work addresses the problem of slow and computationally expensive simulations for engineers, enabling rapid, high-fidelity structural analyses to support design optimization and decision-making, though it is an incremental improvement by combining existing methods.
The paper tackled the challenge of nonlinear structural analysis for complex 3D geometries and loads by developing Point-DeepONet, a deep operator network that integrates PointNet, achieving a coefficient of determination of 0.987 for displacement and 0.923 for von Mises stress while being about 400 times faster than finite element methods.
Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization, uncertainty quantification, and real-time control. Conventional deep learning surrogates, such as convolutional neural networks (CNNs), physics-informed neural networks (PINNs), and fourier neural operators (FNOs), face challenges with complex non-parametric three-dimensional (3D) geometries, directionally varying loads, and high-fidelity predictions on unstructured meshes. This work presents Point-DeepONet, an operator-learning-based surrogate that integrates PointNet into the DeepONet framework. By directly processing non-parametric point clouds and incorporating signed distance functions (SDF) for geometric context, Point-DeepONet accurately predicts three-dimensional displacement and von Mises stress fields without mesh parameterization or retraining. Trained using only about 5,000 nodes (2.5% of the original 200,000-node mesh), Point-DeepONet can still predict the entire mesh at high fidelity, achieving a coefficient of determination reaching 0.987 for displacement and 0.923 for von Mises stress under a horizontal load case. Compared to nonlinear finite element analyses that require about 19.32 minutes per case, Point-DeepONet provides predictions in mere seconds-approximately 400 times faster-while maintaining excellent scalability and accuracy with increasing dataset sizes. These findings highlight the potential of Point-DeepONet to enable rapid, high-fidelity structural analyses, ultimately supporting more effective design exploration and informed decision-making in complex engineering workflows.