Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions
This work addresses the problem of modeling high-dimensional piecewise continuous functions for applications like engineering or scientific simulations, representing an incremental improvement over conventional Jump Gaussian Processes.
The paper tackles surrogate modeling of high-dimensional piecewise continuous functions by introducing Deep Jump Gaussian Processes (DJGP), which adds a locally linear projection layer to Jump Gaussian Processes to capture local subspace structures, resulting in superior predictive accuracy and more reliable uncertainty quantification compared to existing methods.
We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of high-dimensional piecewise continuous functions. DJGP overcomes the limitations of conventional Jump Gaussian Processes in high-dimensional input spaces by adding a locally linear projection layer to Jump Gaussian Processes. This projection uses region-specific matrices to capture local subspace structures, naturally complementing the localized nature of JGP, a variant of local Gaussian Processes. To control model complexity, we place a Gaussian Process prior on the projection matrices, allowing them to evolve smoothly across the input space. The projected inputs are then modeled with a JGP to capture piecewise continuous relationships with the response. This yields a distinctive two-layer deep learning of GP/JGP. We further develop a scalable variational inference algorithm to jointly learn the projection matrices and JGP hyperparameters. Experiments on synthetic and benchmark datasets demonstrate that DJGP delivers superior predictive accuracy and more reliable uncertainty quantification compared to existing approaches.