Gradient-enhanced multifidelity neural networks for high-dimensional function approximation
Gradient-enhanced multifidelity neural networks for high-dimensional function approximation
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DOI：
10.1115/detc2021-70502
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
J. Nagawkar;Leifur Þ. Leifsson
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文献类型：
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作者：
J. Nagawkar;Leifur Þ. Leifsson
在这项工作中，提出了一种新的多保真度机器学习（ML）算法，梯度增强的多保真度神经网络（GEMFNN）算法。这是梯度增强神经网络（GENN）算法的多保真度扩展，因为它使用多个保真度级别的函数和梯度信息来进行函数近似。它的构造类似于多保真度神经网络（MFNN）算法。该算法进行了测试，三个分析功能，一个，两个，和20个变量的功能。它的性能相比，神经网络（NN），GENN，和MFNN的性能，在所需的样本数量达到0.99的决定系数（R2）的全球准确度。结果表明，GEMFNN在一维、二维和20维情况下分别需要18个、120个和600个高保真样本才能满足目标精度。NN在一个变量的情况下表现最好，只需要10个样本，而GENN在两个变量的情况下表现最好，需要120个样本。GEMFNN在20个变量的情况下工作得最好，同时需要的样本比最接近的竞争对手GENN少近8倍。对于这种情况，NN和MFNN即使在使用10，000个高保真样本后也没有达到目标全局精度。这项工作证明了在高维问题的NN中使用梯度和多保真度信息的好处。
In this work, a novel multifidelity machine learning (ML) algorithm, the gradient-enhanced multifidelity neural networks (GEMFNN) algorithm, is proposed. This is a multifidelity extension of the gradient-enhanced neural networks (GENN) algorithm as it uses both function and gradient information available at multiple levels of fidelity to make function approximations. Its construction is similar to the multifidelity neural networks (MFNN) algorithm. The proposed algorithm is tested on three analytical functions, a one, two, and a 20 variable function. Its performance is compared to the performance of neural networks (NN), GENN, and MFNN, in terms of the number of samples required to reach a global accuracy of 0.99 of the coefficient of determination (R2). The results showed that GEMFNN required 18, 120, and 600 high-fidelity samples for the one, two, and 20 dimensional cases, respectively, to meet the target accuracy. NN performed best on the one variable case, requiring only ten samples, while GENN worked best on the two variable case, requiring 120 samples. GEMFNN worked best for the 20 variable case, while requiring nearly eight times fewer samples than its nearest competitor, GENN. For this case, NN and MFNN did not reach the target global accuracy even after using 10,000 high-fidelity samples. This work demonstrates the benefits of using gradient as well as multifidelity information in NN for high-dimensional problems.