mlsanityData to 7 Oct 2026

Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities

arXiv 2102.13403 ↗First posted 26 Feb 2021math.NA cs.LG cs.NAcited by 31

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Abstract (arXiv)

Highly accurate numerical or physical experiments are often time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide satisfactory model results. Multi-fidelity methods deal with such problems by incorporating information from other sources, which are ideally well-correlated with the high-fidelity data, but can be obtained at a lower cost. By leveraging correlations between different data sets, multi-fidelity methods often yield superior generalization when compared to models based solely on a small amount of high-fidelity data. In this work, we present the use of artificial neural networks applied to multi-fidelity regression problems. By elaborating a few existing approaches, we propose new neural network architectures for multi-fidelity regression. The introduced models are compared against a traditional multi-fidelity scheme, co-kriging. A collection of artificial benchmarks are presented to measure the performance of the analyzed models. The results show that cross-validation in combination with Bayesian optimization consistently leads to neural network models that outperform the co-kriging scheme. Additionally, we show an application of multi-fidelity regression to an engineering problem. The propagation of a pressure wave into an acoustic horn with parametrized shape and frequency is considered, and the index of reflection intensity is approximated using the multi-fidelity models. A finite element model and a reduced basis model are adopted as the high- and low-fidelity, respectively. It is shown that the multi-fidelity neural network returns outputs that achieve a comparable accuracy to those from the expensive, full-order model, using only very few full-order evaluations combined with a larger amount of inaccurate but cheap evaluations of a reduced order model.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 11 of its 47 references that are in the map. First posted on arXiv 26 Feb 2021.

Builds on

11 of 47 references.

References · 11

  1. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  2. 2017Deep Neural Networks as Gaussian Processescited by 617
  3. 2019Generalizing from a Few Examples: A Survey on Few-Shot Learningcited by 462
  4. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
  5. 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 141
  6. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
  7. 2020Multi-fidelity Bayesian Neural Networks: Algorithms and Applicationscited by 59
  8. 2019Deep Gaussian Processes for Multi-fidelity Modelingcited by 48
  9. 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
  10. 2016Deep Multi-fidelity Gaussian Processescited by 15
  11. 2014Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamicscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 7; 2024: 7; 2025: 7; 2026: 6.

31 papers.

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  1. 2022Multi-fidelity surrogate modeling using long short-term memory networkscited by 18
  2. 2023Multi-fidelity reduced-order surrogate modelingcited by 18
  3. 2021An extended physics informed neural network for preliminary analysis of parametric optimal control problemscited by 15
  4. 2022Multi-fidelity Hierarchical Neural Processescited by 15
  5. 2023A DeepONet multi-fidelity approach for residual learning in reduced order modelingcited by 14
  6. 2024Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modelingcited by 13
  7. 2023Disentangled Multi-Fidelity Deep Bayesian Active Learningcited by 11
  8. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  9. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  10. 2023Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equationscited by 8
  11. 2022Multifidelity data fusion in convolutional encoder/decoder networkscited by 5
  12. 2023Residual Multi-Fidelity Neural Network Computingcited by 5
19 more
  1. 2024Practical multi-fidelity machine learning: fusion of deterministic and Bayesian modelscited by 4
  2. 2024Multifidelity linear regression for scientific machine learning from scarce datacited by 3
  3. 2024Multi-Fidelity Bayesian Neural Network for Uncertainty Quantification in Transonic Aerodynamic Loadscited by 2
  4. 2025Progressive multi-fidelity learning with neural networks for physical system predictionscited by 2
  5. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  6. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1
  7. 2025Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networkscited by 1
  8. 2026Multifidelity Surrogate Modeling of Depressurized Loss of Forced Cooling in High-temperature Gas Reactorscited by 1
  9. 2026Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurementscited by 1
  10. 2023An iterative multi-fidelity approach for model order reduction of multi-dimensional input parametric PDE systemscited by 0
  11. 2023Differentiable Multi-Fidelity Fusion: Efficient Learning of Physics Simulations with Neural Architecture Search and Transfer Learningcited by 0
  12. 2024Open-Source High-Speed Flight Surrogate Modeling Frameworkcited by 0
  13. 2025On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditionscited by 0
  14. 2025Projection-based multifidelity linear regression for data-scarce applicationscited by 0
  15. 2025Personalized Treatment Outcome Prediction from Scarce Data via Dual-Channel Knowledge Distillation and Adaptive Fusioncited by 0
  16. 2025Multi-fidelity aerodynamic data fusion by autoencoder transfer learningcited by 0
  17. 2026FilDeep: Learning Large Deformations of Elastic-Plastic Solids with Multi-Fidelity Datacited by 0
  18. 2026Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equationscited by 0
  19. 2026A Data-Efficient Analytical Prior Machine Learning Framework for Sound Reduction Frequency Prediction in Helmholtz Resonatorscited by 0