Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries

Abstract

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide design insights. Nevertheless, few available NNs can handle solution prediction on varying 3D shapes. We present a novel deep operator network (DeepONet) variant called Geom-DeepONet, which encodes parameterized 3D geometries and predicts full-field solutions on an arbitrary number of nodes. To the best of the authors' knowledge, this is the first attempt in the literature and is our primary novelty. In addition to expressing shapes using mesh coordinates, the signed distance function for each node is evaluated and used to augment the inputs to the trunk network of the Geom-DeepONet, thereby capturing both explicit and implicit representations of the 3D shapes. The powerful geometric encoding capability of a sinusoidal representation network (SIREN) is also exploited by replacing the classical feedforward neural networks in the trunk with SIREN. Additional data fusion between the branch and trunk networks is introduced by an element-wise product. A numerical benchmark was conducted to compare Geom-DeepONet to PointNet and vanilla DeepONet, where results show that our architecture trains fast with a small memory footprint and yields the most accurate results among the three with less than 2 MPa stress error. Results show a much lower generalization error of our architecture on unseen dissimilar designs than vanilla DeepONet. Once trained, the model can predict vector solutions, and speed can be over $10^5$ times faster than implicit finite element simulations for large meshes.

References in corpus (8)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data
• A physics-informed variational DeepONet for predicting the crack path in brittle materials
• A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries
• Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads
• Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads
• A deep learning energy-based method for classical elastoplasticity
• On the use of graph neural networks and shape-function-based gradient computation in the deep energy method

Cited by in corpus (7)

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• Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations
• Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving
• A Spectral-based Physics-informed Finite Operator Learning for Prediction of Mechanical Behavior of Microstructures
• Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materials
• Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditions
• Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet-Transolver Framework