# Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes

arXiv: https://arxiv.org/abs/2006.15924 · HTML: https://mlsanity.com/paper/2006.15924/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 16 of 16)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation](https://mlsanity.com/paper/2106.13790/) (2021)
- [Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains](https://mlsanity.com/paper/2202.12636/) (2022)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [Cost-effective Framework for Gradual Domain Adaptation with Multifidelity](https://mlsanity.com/paper/2202.04359/) (2022)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Multi-fidelity power flow solver](https://mlsanity.com/paper/2205.13362/) (2022)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Multi-fidelity surrogate with heterogeneous input spaces for modeling melt pools in laser-directed energy deposition](https://mlsanity.com/paper/2403.13136/) (2024)
- [Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process](https://mlsanity.com/paper/2407.11268/) (2024)
- [MF-GLaM: A multifidelity stochastic emulator using generalized lambda models](https://mlsanity.com/paper/2507.10303/) (2025)
- [R^2-HGP: A Double-Regularized Gaussian Process for Heterogeneous Transfer Learning](https://mlsanity.com/paper/2512.10258/) (2025)

## Abstract (arXiv)

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multifidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.