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

arXiv: https://arxiv.org/abs/2412.18362 · HTML: https://mlsanity.com/paper/2412.18362/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems](https://mlsanity.com/paper/2203.00003/) (2022)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Dataset](https://mlsanity.com/paper/2406.09047/) (2024)
- [Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profiles](https://mlsanity.com/paper/2306.00810/) (2023)
- [Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading](https://mlsanity.com/paper/2303.18055/) (2023)
- [Bayesian Mesh Optimization for Graph Neural Networks to Enhance Engineering Performance Prediction](https://mlsanity.com/paper/2406.01996/) (2024)
- [A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain](https://mlsanity.com/paper/2203.08150/) (2022)

## Built on by (most cited first, 10 of 10)

- [DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulations](https://mlsanity.com/paper/2501.13350/) (2025)
- [ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning](https://mlsanity.com/paper/2602.11626/) (2026)
- [Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operators](https://mlsanity.com/paper/2503.04649/) (2025)
- [DeepONet-accelerated Bayesian inversion for moving boundary problems](https://mlsanity.com/paper/2512.20268/) (2025)
- [Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries](https://mlsanity.com/paper/2605.00760/) (2026)
- [EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs](https://mlsanity.com/paper/2606.03260/) (2026)
- [Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges](https://mlsanity.com/paper/2606.20015/) (2026)
- [SplineNet: An Isogeometric Deep Learning Method for Complex Shells](https://mlsanity.com/paper/2607.06026/) (2026)
- [PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations](https://mlsanity.com/paper/2607.08025/) (2026)
- [Feature Interaction Modeling for Neural Operators](https://mlsanity.com/paper/2607.28762/) (2026)

## 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.