Gaussian Process Model with Tensorial Inputs and Its Application to the Design of 3D Printed Antennas

TL;DR

This paper introduces a Gaussian process model with a new kernel that effectively incorporates 3D spatial information from 3D printed designs, enhancing simulation-based optimization for complex engineering problems like antenna design.

Contribution

It proposes a novel GP kernel embedding spatial information, enabling better modeling of 3D printed objects in design optimization tasks.

Findings

The new kernel improves modeling accuracy for 3D printed antenna designs.

Numerical examples demonstrate enhanced optimization performance.

The method integrates spatial data into GP frameworks effectively.

Abstract

In simulation-based engineering design with time-consuming simulators, Gaussian process (GP) models are widely used as fast emulators to speed up the design optimization process. In its most commonly used form, the input of GP is a simple list of design parameters. With rapid development of additive manufacturing (also known as 3D printing), design inputs with 2D/3D spatial information become prevalent in some applications, for example, neighboring relations between pixels/voxels and material distributions in heterogeneous materials. Such spatial information, vital to 3D printed designs, is hard to incorporate into existing GP models with common kernels such as squared exponential or Mat\'ern. In this work, we propose to embed a generalized distance measure into a GP kernel, offering a novel and convenient technique to incorporate spatial information from freeform 3D printed designs into the GP framework. The proposed method allows complex design problems for 3D printed objects to take advantage of a plethora of tools available from the GP surrogate-based simulation optimization such as designed experiments and GP-based optimizations including Bayesian optimization. We investigate the properties of the proposed method and illustrate its performance by several numerical examples of 3D printed antennas. The dataset is publicly available at: https://github.com/xichennn/GP_dataset.