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

arXiv: https://arxiv.org/abs/2404.11965 · HTML: https://mlsanity.com/paper/2404.11965/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 79 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 23 of 23)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Kernel Flows: from learning kernels from data into the abyss](https://mlsanity.com/paper/1808.04475/) (2018)
- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Multilevel Delayed Acceptance MCMC](https://mlsanity.com/paper/2202.03876/) (2022)
- [EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions](https://mlsanity.com/paper/2106.04618/) (2021)
- [Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection](https://mlsanity.com/paper/2207.01242/) (2022)
- [Leveraging Trust for Joint Multi-Objective and Multi-Fidelity Optimization](https://mlsanity.com/paper/2112.13901/) (2021)
- [Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion](https://mlsanity.com/paper/1812.06467/) (2018)
- [Sharp Calibrated Gaussian Processes](https://mlsanity.com/paper/2302.11961/) (2023)
- [Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification](https://mlsanity.com/paper/2211.10835/) (2022)
- [Multi-fidelity Constrained Optimization for Stochastic Black Box Simulators](https://mlsanity.com/paper/2311.15137/) (2023)

## Built on by (most cited first, 4 of 4)

- [QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules](https://mlsanity.com/paper/2406.14149/) (2024)
- [Assessing Non-Nested Configurations of Multifidelity Machine Learning for Quantum-Chemical Properties](https://mlsanity.com/paper/2407.17087/) (2024)
- [FIRE: Multi-fidelity Regression with Distribution-conditioned In-context Learning using Tabular Foundation Models](https://mlsanity.com/paper/2601.22371/) (2026)
- [Real-Time Performance Analysis of Multi-Fidelity Residual Physics-Informed Neural Process-Based State Estimation for Robotic Systems](https://mlsanity.com/paper/2511.08231/) (2025)

## Abstract (arXiv)

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.