On Transfer Learning of Neural Networks Using Bi-Fidelity Data for Uncertainty Propagation

Subhayan De, Jolene Britton, Matthew Reynolds, Ryan Skinner, Kenneth Jansen, Alireza Doostan

Research output: Contribution to journalArticlepeer-review

38 Scopus Citations


Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantifi-cation applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high-and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

Original languageAmerican English
Pages (from-to)543-573
Number of pages31
JournalInternational Journal for Uncertainty Quantification
Issue number6
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 by Begell House, Inc. www.begellhouse.com.

NREL Publication Number

  • NREL/JA-2C00-75670


  • Gaussian process regression
  • Neural network
  • Scientific machine learning
  • Transfer learning
  • Uncertainty propagation


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