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

arXiv: https://arxiv.org/abs/2407.15877 · HTML: https://mlsanity.com/paper/2407.15877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [Tensor Regression Meets Gaussian Processes](https://mlsanity.com/paper/1710.11345/) (2017)
- [Deep Gaussian Processes with Convolutional Kernels](https://mlsanity.com/paper/1806.01655/) (2018)
- [Bayesian Tensor-on-Tensor Regression with Efficient Computation](https://mlsanity.com/paper/2210.11363/) (2022)
- [Tensor Gaussian Process with Contraction for Multi-Channel Imaging Analysis](https://mlsanity.com/paper/2301.11203/) (2023)

## Abstract (arXiv)

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/GPdataset.