Multi-fidelity meta modeling using composite neural network with online adaptive basis technique. (English) Zbl 1507.65026
Summary: A composite neural network (NN) is a way to improve the reliability of a prediction field by implementing a multi-fidelity model when high-fidelity data are extremely limited. The reliability of the composite NN depends highly on the quantity and quality of low-fidelity data. Satisfying both issues simultaneously is difficult in engineering practices even if low-fidelity data are considered. With this motivation, we suggest a strategy for ameliorating low-fidelity data to efficiently improve the prediction fields of a composite NN. In the proposed strategy, a reduced-order modeling (ROM) is used to supply a large number of low-fidelity data with relatively low computational costs. To decrease ROM errors that may decisively hinder the training of a cross-correlation between low-fidelity and high-fidelity data, the low-fidelity data are updated using an efficient adaptive basis technique. The adaptive basis in this work is calculated by optimizing the local error data to avoid huge computational costs. As a result, the low-fidelity data can better reflect the trend while satisfying the condition in which the low-fidelity data should be sufficiently provided through an efficient procedure. Furthermore, the strategy applied in this study is conducted without any modifications of the given high-fidelity data. Hence, even if high-fidelity data may no longer be obtained, it is possible to efficiently obtain the high-quality prediction field of the composite NN. A detailed strategy is proposed herein, and its performance is evaluated through various numerical examples.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 68T07 | Artificial neural networks and deep learning |
Keywords:
machine learning; online adaptive basis method; composite neural network; multi-fidelity approach; reduced order modeling; data-driven modelingReferences:
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