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.

中文翻译：

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使用人工神经网络进行多保真度回归：有效近似基于参数的输出量

高度精确的数值或物理实验通常很耗时或昂贵。当时间或预算限制禁止生成其他数据时，可用样本的数量可能会太有限而无法提供令人满意的模型结果。多保真方法通过合并来自其他来源的信息来解决此类问题，这些信息在理想情况下与高保真数据具有很好的相关性，但可以以较低的成本获得。与仅基于少量高保真度数据的模型相比，通过利用不同数据集之间的相关性，多保真度方法通常可以产生出色的概括性。在这项工作中，我们介绍了将人工神经网络应用于多保真度回归问题。通过阐述一些现有方法，我们提出了用于多保真度回归的新神经网络架构。将引入的模型与传统的多保真度方案（共同克里金法）进行了比较。提出了一组人为基准，以衡量所分析模型的性能。结果表明，交叉验证与贝叶斯优化相结合，始终能够产生优于协同克里格方案的神经网络模型。此外，我们展示了多保真度回归在工程问题中的应用。考虑将压力波传播到具有参数化形状和频率的声学号筒中，并使用多保真度模型来估算反射强度的指标。高保真度和低保真度分别采用了有限元模型和缩减基数模型。