mlsanityData to 7 Oct 2026

Deep Gaussian Processes for Multi-fidelity Modeling

arXiv 1903.07320 ↗First posted 18 Mar 2019stat.ML cs.LGcited by 48

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Abstract (arXiv)

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both fundamental machine learning procedures such as Bayesian optimization, as well as more practical science and engineering applications. In this paper we develop a novel multi-fidelity model which treats layers of a deep Gaussian process as fidelity levels, and uses a variational inference scheme to propagate uncertainty across them. This allows for capturing nonlinear correlations between fidelities with lower risk of overfitting than existing methods exploiting compositional structure, which are conversely burdened by structural assumptions and constraints. We show that the proposed approach makes substantial improvements in quantifying and propagating uncertainty in multi-fidelity set-ups, which in turn improves their effectiveness in decision making pipelines.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Mar 2019.

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Citing papers per year: 2021: 13; 2022: 9; 2023: 6; 2024: 11; 2025: 3; 2026: 6.

48 papers.

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  1. 2022Recent Advances in Bayesian Optimizationcited by 74
  2. 2021GIBBON: General-purpose Information-Based Bayesian OptimisatioNcited by 47
  3. 2022Machine Learning in Aerodynamic Shape Optimizationcited by 39
  4. 2023Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisationcited by 32
  5. 2021Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantitiescited by 31
  6. 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 31
  7. 2021Conditioning Sparse Variational Gaussian Processes for Online Decision-makingcited by 23
  8. 2022Multi-fidelity surrogate modeling using long short-term memory networkscited by 18
  9. 2024Operator Learning with Gaussian Processescited by 18
  10. 2022Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimizationcited by 16
  11. 2022Multi-fidelity Hierarchical Neural Processescited by 15
  12. 2024Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modelingcited by 13
36 more
  1. 2023Disentangled Multi-Fidelity Deep Bayesian Active Learningcited by 11
  2. 2023A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Samplingcited by 10
  3. 2021Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulationscited by 8
  4. 2021Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modelingcited by 8
  5. 2022Infinite-Fidelity Coregionalization for Physical Simulationcited by 7
  6. 2021Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networkscited by 6
  7. 2024Machine learning for industrial sensing and control: A survey and practical perspectivecited by 6
  8. 2021Safe Real-Time Optimization using Multi-Fidelity Gaussian Processescited by 5
  9. 2024Multi-Fidelity Methods for Optimization: A Surveycited by 5
  10. 2024Multi-fidelity Gaussian process surrogate modeling for regression problems in physicscited by 4
  11. 2024Practical multi-fidelity machine learning: fusion of deterministic and Bayesian modelscited by 4
  12. 2025Verification and Validation for Trustworthy Scientific Machine Learningcited by 4
  13. 2021On the Correspondence between Gaussian Processes and Geometric Harmonicscited by 3
  14. 2023GAR: Generalized Autoregression for Multi-Fidelity Fusioncited by 3
  15. 2023Diffusion-Generative Multi-Fidelity Learning for Physical Simulationcited by 3
  16. 2024Multi-fidelity Machine Learning for Uncertainty Quantification and Optimizationcited by 3
  17. 2021Gemini: Dynamic Bias Correction for Autonomous Experimentation and Molecular Simulationcited by 2
  18. 2021Compressed particle methods for expensive models with application in Astronomy and Remote Sensingcited by 2
  19. 2022Deep Gaussian Process-based Multi-fidelity Bayesian Optimization for Simulated Chemical Reactorscited by 2
  20. 2021On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approachcited by 1
  21. 2021GAN-MDF: A Method for Multi-fidelity Data Fusion in Digital Twinscited by 1
  22. 2022On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernelcited by 1
  23. 2022Multi-fidelity Gaussian Process for Biomanufacturing Process Modeling with Small Datacited by 1
  24. 2024Uncertainty-aware multi-fidelity surrogate modeling with noisy datacited by 1
  25. 2024Multi-fidelity surrogate with heterogeneous input spaces for modeling melt pools in laser-directed energy depositioncited by 1
  26. 2024Multifidelity digital twin for real-time monitoring of structural dynamics in aquaculture net cagescited by 1
  27. 2026FIRE: Multi-fidelity Regression with Distribution-conditioned In-context Learning using Tabular Foundation Modelscited by 1
  28. 2023Differentiable Multi-Fidelity Fusion: Efficient Learning of Physics Simulations with Neural Architecture Search and Transfer Learningcited by 0
  29. 2024Gradient-enhanced deep Gaussian processes for multifidelity modellingcited by 0
  30. 2025MF-GLaM: A multifidelity stochastic emulator using generalized lambda modelscited by 0
  31. 2025Real-Time Performance Analysis of Multi-Fidelity Residual Physics-Informed Neural Process-Based State Estimation for Robotic Systemscited by 0
  32. 2026MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weightingcited by 0
  33. 2026Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimizationcited by 0
  34. 2026Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Datacited by 0
  35. 2026On the Brittleness of Maximum Likelihood Estimation for Gaussian Process Hyperparameter Optimizationcited by 0
  36. 2026MF-SCBO : Multi-fidelity Scalable Constrained Bayesian Optimizationcited by 0