Physical simulations based on partial differential equations typically generate spatial fields results, which are utilized to calculate specific properties of a system for engineering design and optimization. Due to the intensive computational burden of the simulations, a surrogate model mapping the low-dimensional inputs to the spatial fields are commonly built based on a relatively small dataset. To resolve the challenge of predicting the whole spatial field, the popular linear model of coregionalization (LMC) can disentangle complicated correlations within the high-dimensional spatial field outputs and deliver accurate predictions. However, LMC fails if the spatial field cannot be well approximated by a linear combination of base functions with latent processes. In this paper, we extend LMC by introducing an invertible neural network to linearize the highly complex and nonlinear spatial fields such that the LMC can easily generalize to nonlinear problems while preserving the traceability and scalability. Several real-world applications demonstrate that E-LMC can exploit spatial correlations effectively, showing a maximum improvement of about 40% over the original LMC and outperforming the other state-of-the-art spatial field models.

介绍了一种将可逆神经网络引入到线性核关联模型中，以便更好地处理非线性问题，并有效地利用空间相关性，表现出了40％左右的最大改进，并胜过其他最先进的空间场模型。

E-LMC: 基于空间协同变异数组的扩展线性核函数模型