mlsanityData to 7 Oct 2026

Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditions

arXiv 2412.18362 ↗First posted 24 Dec 2024cs.LG cs.AIcited by 10

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Abstract (arXiv)

Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization and real-time control. Conventional deep learning surrogates often struggle with complex, non-parametric three-dimensional (3D) geometries and directionally varying loads. This work presents Point-DeepONet, an operator-learning-based surrogate that integrates PointNet into the DeepONet framework to learn a mapping from non-parametric geometries and variable load conditions to physical response fields. By leveraging PointNet to learn a geometric representation from raw point clouds, our model circumvents the need for manual parameterization. This geometric embedding is then synergistically fused with load conditions within the DeepONet architecture to accurately predict three-dimensional displacement and von Mises stress fields. Trained on a large-scale dataset, Point-DeepONet demonstrates high fidelity, achieving a coefficient of determination (R^2) reaching 0.987 for displacement and 0.923 for von Mises stress. Furthermore, to rigorously validate its generalization capabilities, we conducted additional experiments on unseen, randomly oriented load directions, where the model maintained exceptional accuracy. 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. These findings, validated through extensive experiments and ablation studies, highlight the potential of Point-DeepONet to enable rapid, high-fidelity structural analyses for complex engineering workflows.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 28 of its 42 references that are in the map. First posted on arXiv 24 Dec 2024.

Builds on

28 of 42 references.

References · 28

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  7. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  8. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
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16 more
  1. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  2. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  3. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  4. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  5. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  6. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  7. 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 47
  8. 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
  9. 2024Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometriescited by 47
  10. 2020A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometriescited by 44
  11. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
  12. 2024DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Datasetcited by 16
  13. 2023Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profilescited by 10
  14. 2023Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loadingcited by 5
  15. 2024Bayesian Mesh Optimization for Graph Neural Networks to Enhance Engineering Performance Predictioncited by 3
  16. 2022A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domaincited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 7.

10 papers.

  1. 2025DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulationscited by 26
  2. 2026ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learningcited by 3
  3. 2025Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operatorscited by 1
  4. 2025DeepONet-accelerated Bayesian inversion for moving boundary problemscited by 0
  5. 2026Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometriescited by 0
  6. 2026EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEscited by 0
  7. 2026Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridgescited by 0
  8. 2026SplineNet: An Isogeometric Deep Learning Method for Complex Shellscited by 0
  9. 2026PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulationscited by 0
  10. 2026Feature Interaction Modeling for Neural Operatorscited by 0