Data Fusion with Latent Map Gaussian Processes

TL;DR

This paper introduces a novel latent-map Gaussian process method for efficient, flexible, and accurate multi-fidelity data fusion, enabling better visualization, calibration, and error detection in engineering modeling.

Contribution

The paper presents a new LMGP-based approach that automatically learns relations among data sources, improves accuracy, reduces costs, and simplifies implementation compared to existing methods.

Findings

Outperforms existing data fusion methods in accuracy.

Enables visualization of data source correlations.

Provides high-precision calibration parameter estimation.

Abstract

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlations between data sources. This visualization allows the user to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the subset of the data sources that are well-correlated. We also develop a new kernel function that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing technologies. We demonstrate the benefits of LMGP-based data fusion by comparing its performance against competing methods on a wide range of examples.