Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
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DOI：
10.1098/rspa.2016.0751
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发表时间：
2017-02-01
影响因子：
3.5
通讯作者：
Karniadakis, G. E.
中科院分区：
文献类型：
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作者：
Perdikaris, P.;Raissi, M.;Karniadakis, G. E.
多保真度建模通过将低成本/低保真度模型的实现与一小组高保真度观察协同组合来实现对感兴趣的量的准确推断。当低保真和高保真模型表现出强相关性时，这特别有效，并且可以导致比仅依赖高保真模型的方法显著的计算增益。然而，在许多实际感兴趣的情况下，低保真模型只能在特定的输入参数范围内与高保真模型很好地相关，并且如果在其有效性范围之外进行探测，则可能返回错误的趋势和错误的预测。在这里，我们提出了一个基于高斯过程回归和非线性自回归方案的概率框架，该框架能够学习可变保真度模型之间复杂的非线性和空间相关的互相关，并且可以有效地防止提供错误趋势的低保真度模型。这引入了一类新的多保真度信息融合算法，提供了一个基本的扩展到现有的线性自回归方法，同时仍然保持相同的算法复杂度和整体计算成本。所提出的方法的性能进行了测试，在几个基准问题，涉及合成和真实的多保真度数据集从计算流体动力学模拟。
Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high- fidelity observations. This is particularly effective when the low-and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent crosscorrelations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multifidelity datasets from computational fluid dynamics simulations.