Geom-DeepONet: A point-cloud-based deep operator network for field predictions on 3D parameterized geometries

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. Results show a much lower generalization error of our architecture on unseen dissimilar designs than vanilla DeepONet. Training the model on 2500 cuboid designs is done within 2 h on a single A100 GPU while generating the training dataset through finite element simulations took about 27 h. Once trained, the model can predict vector fields and a single prediction can be over 105 times faster than its corresponding implicit finite element simulation if the mesh is large. The ability of the proposed model to perform efficient and accurate field predictions on variable 3D geometries, especially those discretized by different nodes and elements, makes it a valuable tool for preliminary performance evaluation and design optimizations and is the most significant contribution of the current work.