<p>Scientific and engineering problems often require an inexpensive surrogate model to aid understanding and the search for promising designs. While Gaussian processes stand out as easy-to-use and interpretable learners in surrogate modeling, conventional Gaussian process models have difficulties in accommodating big datasets, qualitative factors, and multi-type responses obtained from different simulators. With the recent increase in database resources, these features have become a common challenge for a growing number of data-driven design applications, such as multiscale topology optimization and the discovery of new compounds in combinatorial materials design. In this paper, we propose a Gaussian process model that can address all three challenges simultaneously. The key idea is to utilize some latent variables and functions obtained through variational inference to facilitate the modeling process. Specifically, the qualitative factors are mapped into a continuous latent space to enable Gaussian process modeling on a mixed-variable dataset. The statistical information of a large training dataset is approximated by a small set of inducing points to improve the scalability. Output response vectors are represented by a linear combination of independent latent functions, forming a more flexible kernel structure to handle multi-type responses. We then introduce several extensions of these models to integrate them into a new synthesized GP model to accommodate big data with qualitative factors and multi-type responses. Comparative studies demonstrate that the proposed model scales well for a large dataset with over data points. The model enjoys a high prediction power for mixed-variable inputs and multi-type responses, which outperforms state-of-the-art machine learning methods without requiring much hyperparameter tuning. Moreover, an interpretable latent space can be obtained from the proposed model to provide insights into the effect of qualitative factors. As a demonstrative case study, an efficient design of a multiscale compliant mechanism with aperiodic microstructures is achieved by integrating the proposed model in topology optimization.</p>

Data-Driven Design via Scalable Gaussian Processes for Multi-Response Big Data With Qualitative Factors

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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