# A graphical multi-fidelity Gaussian process model, with application to emulation of expensive computer simulations

@inproceedings{Ji2021AGM, title={A graphical multi-fidelity Gaussian process model, with application to emulation of expensive computer simulations}, author={Yi Ji and Simon Mak and Derek Soeder and Jean-François Paquet and Steffen A. Bass}, year={2021} }

With advances in scientific computing and mathematical modeling, complex phenomena can now be reliably simulated. Such simulations can however be very timeintensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of varying accuracies (or fidelities) to train an efficient predictive model (or emulator) for the expensive simulator. In complex problems, simulation data with different fidelities are often connected scientifically via a…

## One Citation

### Stacking designs: designing multi-fidelity computer experiments with confidence

- Computer Science
- 2022

The stacking design provides a sequential approach for designing multi-ﬁdelity runs such that a desired prediction error of (cid:15) > 0 is met under regularity conditions and proves a novel cost complexity theorem which establishes a bound on the computation cost needed to ensure a prediction bound.

## References

SHOWING 1-10 OF 67 REFERENCES

### Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes

- Computer ScienceSIAM/ASA J. Uncertain. Quantification
- 2020

New closed-form formulas are derived to compute the means and variances of predictive distributions in autoregressive cokriging models that only depend on correlation parameters and several objective priors are developed that are shown to yield proper posterior distributions.

### Deep Gaussian Processes for Multi-fidelity Modeling

- Computer ScienceArXiv
- 2019

A novel multi-fidelity model is developed which treats layers of a deep Gaussian process as fidelity levels, and uses a variational inference scheme to propagate uncertainty across them, allowing for capturing nonlinear correlations between fidelities with lower risk of overfitting than existing methods exploiting compositional structure.

### RECURSIVE CO-KRIGING MODEL FOR DESIGN OF COMPUTER EXPERIMENTS WITH MULTIPLE LEVELS OF FIDELITY

- Computer Science
- 2012

It is proved that the predictive mean and the variance of the presented approach are identical to the ones of the original co-kriging model, and the proposed approach has a reduced computational complexity compared to the previous one.

### An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations

- PhysicsJournal of the American Statistical Association
- 2018

ABSTRACT In the quest for advanced propulsion and power-generation systems, high-fidelity simulations are too computationally expensive to survey the desired design space, and a new design…

### Review of multi-fidelity models

- Computer Science
- 2016

It is found that time savings are highly problem dependent and that MFM methods provided time savings up to 90% and guidelines for authors to present their MFM savings in a way that is useful to future MFM users are included.

### Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

A probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends is put forth.

### Bayesian Analysis of Hierarchical Multifidelity Codes

- Computer ScienceSIAM/ASA J. Uncertain. Quantification
- 2013

A new approach to estimating the model parameters which provides a closed form expression for an important parameter of the model (the scale factor), a reduction of the numerical complexity by simplifying the covariance matrix inversion, and a new Bayesian modeling that gives an explicit representation of the joint distribution of the parameters and that is not computationally expensive.

### Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology

- Computer Science
- 2011

This work proposes a new model that uses a combination of low-order regression terms and compactly supported correlation functions to recreate the desired predictive behavior of the emulator at a fraction of the computational cost.

### MFNets: MULTI-FIDELITY DATA-DRIVEN NETWORKS FOR BAYESIAN LEARNING AND PREDICTION

- Computer Science
- 2020

It is demonstrated that MFNets can fuse heterogeneous data sources arising from simulations with different parameterizations and derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models, to be the first such derivation.

### MFNets: Learning network representations for multifidelity surrogate modeling

- Computer ScienceArXiv
- 2020

This paper formulates a network of surrogate models whose relationships are defined via localized scalings and shifts that can have general structure, and can represent a significantly greater variety of modeling relationships than the hierarchical/recursive networks used in the current state of the art.