使用人工神经网络的多保真度回归：依赖于参数的输出量的有效近似
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
摘要：
高精度的数值或物理实验通常是耗时或昂贵的。当时间或预算限制禁止生成额外数据时，可用样本的数量可能太有限，无法提供令人满意的模型结果。多保真度方法通过合并来自其他来源的信息来处理这些问题，这些信息与高保真数据理想地良好相关，但可以以较低的成本获得。通过利用不同数据集之间的相关性，与仅基于少量高保真数据的模型相比，多保真度方法通常会产生更好的泛化能力。在这项工作中，我们提出了使用人工神经网络应用于多保真度回归问题。通过阐述一些现有的方法，我们提出了新的神经网络架构的多保真度回归。引入的模型进行了比较，对传统的多保真度计划，协同克里格。一系列的人工基准来衡量所分析的模型的性能。结果表明，交叉验证与贝叶斯优化相结合，始终导致神经网络模型的性能优于协同克里金方案。此外，我们展示了多保真度回归的工程问题的应用。考虑了压力波在具有参数化形状和频率的声喇叭中的传播，并利用多保真度模型近似了反射强度指数。分别采用有限元模型和缩减基模型作为高保真度和低保真度。结果表明，多保真度神经网络返回的输出，实现了可比的精度从昂贵的，全阶模型，只使用很少的全阶评估结合大量的不准确，但便宜的评估降阶模型。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
