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

TL;DR

Point-DeepONet introduces a hybrid operator-learning surrogate that fuses PointNet with DeepONet to perform fully nonlinear elastoplastic analyses on non-parametric 3D geometries under directionally varying loads. By processing point clouds and incorporating signed distance functions, the method predicts displacement and von Mises stress directly on the original FE mesh with high accuracy (e.g., $R^2$ up to 0.987 for displacement) while delivering inference times orders of magnitude faster than conventional FE analyses. The approach uses a resampling strategy to enable batched training and demonstrates robustness across resampling densities, dataset sizes, and input configurations, outperforming PointNet and DeepONet in most settings. This work enables rapid, high-fidelity structural analysis and design exploration for complex geometries, with potential extensions to anisotropic materials, time-dependent loading, PINNs, and transfer learning for broader applicability.

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.

Figures (16)

• Figure 1: Illustration of the nonlinear static analysis setup for the bracket under different load cases. (a) Bracket geometry and load direction overview: vertical, horizontal, and diagonal load cases. (b) Identification of bolted and loaded interfaces in the bracket. (c) Schematic of boundary conditions and constraints applied in the analysis.
• Figure 2: Visualization of dataset distribution by load direction. (a) Frequency distribution of load cases across vertical, horizontal, and diagonal directions. (b) Scatter plot showing elapsed time versus node count for vertical, horizontal, and diagonal load cases.
• Figure 3: Distribution of structural properties in the dataset: (a) Node count distribution, representing the complexity of the mesh geometries used in FEA analysis; (b) Mass distribution, capturing the range of structural weights across different bracket geometries.
• Figure 4: Dataset characteristics for training and validation sets. (a) Node count distribution with violin plot insets showing spread. (b) Mass distribution with violin plot insets showing variability. (c) Sampled images from the training set by mass. (d) Sampled images from the validation set by mass.
• Figure 5: PointNet architecture.