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In the kriging and Gaussian process regression frameworks, the covariance kernel plays a fundamental role. The construction of flexible spatiotemporal regression kernels is essential for capturing dynamic physical processes. Hence, kernels derivable from stochastic equations of motion are in high demand for their effectiveness in modeling complex systems. We review the few cases of known purely spatial covariance kernels derived from stochastic differential equations. On the other hand, constructing non-separable spatiotemporal kernels derivable from physical equations presents significant challenges. We focus on the recently developed hybrid spectral method which combines temporal dependence derived from physical systems with observation-informed dispersion relations.

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Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes Based on the Hybrid Spectral Method

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Dionissios T. Hristopulos

摘要

In the kriging and Gaussian process regression frameworks, the covariance kernel plays a fundamental role. The construction of flexible spatiotemporal regression kernels is essential for capturing dynamic physical processes. Hence, kernels derivable from stochastic equations of motion are in high demand for their effectiveness in modeling complex systems. We review the few cases of known purely spatial covariance kernels derived from stochastic differential equations. On the other hand, constructing non-separable spatiotemporal kernels derivable from physical equations presents significant challenges. We focus on the recently developed hybrid spectral method which combines temporal dependence derived from physical systems with observation-informed dispersion relations.