MF-GLaM: A multifidelity stochastic emulator using generalized lambda models

TL;DR

This paper introduces MF-GLaM, a multifidelity stochastic emulator that efficiently models the full response distribution of high-fidelity simulators using lower-fidelity data, improving accuracy and reducing costs.

Contribution

The paper develops MF-GLaM, a novel multifidelity generalized lambda model that emulates stochastic simulator distributions without internal access or multiple replications.

Findings

MF-GLaM outperforms single-fidelity models in accuracy.

MF-GLaM reduces computational cost while maintaining performance.

Validated on synthetic and earthquake simulation examples.

Abstract

Stochastic simulators exhibit intrinsic stochasticity due to unobservable, uncontrollable, or unmodeled input variables, resulting in random outputs even at fixed input conditions. Such simulators are common across various scientific disciplines; however, emulating their entire conditional probability distribution is challenging, as it is a task traditional deterministic surrogate modeling techniques are not designed for. Additionally, accurately characterizing the response distribution can require prohibitively large datasets, especially for computationally expensive high-fidelity (HF) simulators. When lower-fidelity (LF) stochastic simulators are available, they can enhance limited HF information within a multifidelity surrogate modeling (MFSM) framework. While MFSM techniques are well-established for deterministic settings, constructing multifidelity emulators to predict the full conditional response distribution of stochastic simulators remains a challenge. In this paper, we propose multifidelity generalized lambda models (MF-GLaMs) to efficiently emulate the conditional response distribution of HF stochastic simulators by exploiting data from LF stochastic simulators. Our approach builds upon the generalized lambda model (GLaM), which represents the conditional distribution at each input by a flexible, four-parameter generalized lambda distribution. MF-GLaMs are non-intrusive, requiring no access to the internal stochasticity of the simulators nor multiple replications of the same input values. We demonstrate the efficacy of MF-GLaM through synthetic examples of increasing complexity and a realistic earthquake application. Results show that MF-GLaMs can achieve improved accuracy at the same cost as single-fidelity GLaMs, or comparable performance at significantly reduced cost.