Point-DeepONet: A Deep Operator Network Integrating PointNet for Nonlinear Analysis of Non-Parametric 3D Geometries and Load Conditions

• URL: http://arxiv.org/abs/2412.18362v1
• Date: Tue, 24 Dec 2024 11:44:58 GMT
• Title: Point-DeepONet: A Deep Operator Network Integrating PointNet for Nonlinear Analysis of Non-Parametric 3D Geometries and Load Conditions
• Abstract summary: This work presents Point-DeepONet, an operator-based geometric surrogate that integrates PointNet into the DeepONet framework.<n>Point-DeepONet accurately predicts three-dimensional displacement and von Mises stress fields without mesh parameterization or retraining.<n>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.
• Score: 1.6574413179773761
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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