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

2024-12-24

AI Summary

Nonlinear structural analysis under variable-direction loads and nonparametric 3D geometries remains challenging; existing methods—including CNNs, PINNs, and FNOs—exhibit limitations in accuracy, generalizability, or computational efficiency. Method: We propose the first end-to-end operator learning framework integrating PointNet with DeepONet, directly accepting raw point clouds and signed distance fields (SDFs) as inputs to predict displacement and von Mises stress fields without meshing or retraining. Contribution/Results: By embedding PointNet into DeepONet, our model jointly encodes geometric and load-direction information, enabling resolution-agnostic generalization. Trained on only 5,000 nodes (2.5% of the original mesh), it achieves R² scores of 0.987 for displacement and 0.923 for stress, with sub-second inference time—accelerating nonlinear finite element analysis by approximately 400×.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• 3D Object Analysis
• Complex Shape Modeling
• Force Prediction

Innovation

• Point-DeepONet
• PointNet and DeepONet Integration
• Efficient 3D Displacement and Stress Prediction