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

arXiv: https://arxiv.org/abs/2507.10303 · HTML: https://mlsanity.com/paper/2507.10303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 59 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 18 of 18)

- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems](https://mlsanity.com/paper/1901.04878/) (2019)
- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)
- [Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes](https://mlsanity.com/paper/2006.15924/) (2020)
- [Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions](https://mlsanity.com/paper/1911.09067/) (2019)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [A spectral surrogate model for stochastic simulators computed from trajectory samples](https://mlsanity.com/paper/2207.05653/) (2022)
- [Seismic fragility analysis using stochastic polynomial chaos expansions](https://mlsanity.com/paper/2208.07747/) (2022)
- [Surrogate modeling with functional nonlinear autoregressive models (F-NARX)](https://mlsanity.com/paper/2410.07293/) (2024)
- [Emulators for stochastic simulation codes](https://mlsanity.com/paper/1406.6348/) (2014)
- [Stochastic simulators based optimization by Gaussian process metamodels -- Application to maintenance investments planning issues](https://mlsanity.com/paper/1512.07060/) (2015)
- [Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty](https://mlsanity.com/paper/2311.00553/) (2023)
- [Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction](https://mlsanity.com/paper/2007.13553/) (2020)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Covariance-free Bi-fidelity Control Variates Importance Sampling for Rare Event Reliability Analysis](https://mlsanity.com/paper/2405.03834/) (2024)

## Abstract (arXiv)

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.