Multi-fidelity Gaussian process surrogate modeling for regression problems in physics

TL;DR

This paper compares and extends multi-fidelity Gaussian process surrogate modeling methods for regression problems in physics, demonstrating their efficiency and limitations across various scenarios.

Contribution

It extends non-linear autoregressive multi-fidelity methods to handle more than two fidelity levels and introduces a structured kernel for delay term incorporation.

Findings

Multi-fidelity methods reduce prediction error for the same computational cost.

Effectiveness of multi-fidelity methods varies across different scenarios.

Proposed enhancements improve modeling flexibility and performance.

Abstract

One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a hierarchy with increasing fidelity, associated with lower error, but increasing cost. In this paper, we compare different multi-fidelity methods employed in constructing Gaussian process surrogates for regression. Non-linear autoregressive methods in the existing literature are primarily confined to two-fidelity models, and we extend these methods to handle more than two levels of fidelity. Additionally, we propose enhancements for an existing method incorporating delay terms by introducing a structured kernel. We demonstrate the performance of these methods across various academic and real-world scenarios. Our findings reveal that multi-fidelity methods generally have a smaller prediction error for the same computational cost as compared to the single-fidelity method, although their effectiveness varies across different scenarios.