An Investigation of Surrogate Models for Efficient Performance-Based Decoding of 3D Point Clouds

Abstract

Abstract This work investigates surrogate modeling techniques for learning to approximate a computationally expensive function evaluation of 3D models. While in the past, 3D point clouds have been a data format that is too high dimensional for surrogate modeling, by leveraging advances in 3D object autoencoding neural networks, these point clouds can be mapped to a one-dimensional latent space. This leads to the fundamental research question: what surrogate modeling technique is most suitable for learning relationships between the 3D geometric features of the objects captured in the encoded latent vector and the physical phenomena captured in the evaluation software? Radial basis functions (RBFs), Kriging, and shallow 1D analogs of popular deep 2D image classification neural networks are investigated in this work. We find the nonintuitive result that departing from neural networks to decode latent representations of 3D objects into performance predictions is far more efficient than using a neural network decoder. In test cases using datasets of aircraft and watercraft 3D models, the non-neural network surrogate models achieve comparable accuracy to the neural network models. We find that an RBF surrogate model is able to approximate the lift and drag coefficients of 234 aircraft models with a mean absolute error of 1.97 × 10−3 and trains in only 3 seconds. Furthermore, the RBF surrogate model is able to rank a set of designs with an average percentile error of less than 8%. In comparison, a 1D ResNet achieves an average absolute error of 1.35 × 103 in 38 min for the same test case. We validate the comparable accuracy of the four techniques through a test case involving 214 3D watercraft models, but we also find that the distribution of the performance values of the data, in particular the presence of many outliers, has a significant negative impact on accuracy. These results contradict a common perception of neural networks as an efficient “one-size-fits-all” solution for learning black-box functions and suggests that even within systems that utilize multiple neural networks, potentially more efficient alternatives should be considered for each network in the system. Depending on the required accuracy of the application, this surrogate modeling approach could be used to approximate an expensive simulation software, or if the tolerance for error is low, it serves as a first pass which can narrow down the number of candidate designs to be analyzed more thoroughly.