E-LMC: Extended Linear Model of Coregionalization for Spatial Field Prediction
This work addresses the problem of efficient spatial field prediction for engineering design and optimization, offering a novel extension to an existing method for handling nonlinear cases.
The paper tackles the challenge of predicting high-dimensional spatial fields from low-dimensional inputs when linear approximations fail, by introducing an invertible neural network to linearize nonlinear fields, resulting in up to 40% improvement over the original LMC and outperforming other state-of-the-art models.
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 present the Extended Linear Model of Coregionalization (E-LMC) by introducing an invertible neural network to linearize the highly complex and nonlinear spatial fields so 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.