[2603.00290] Scalable Gaussian process modeling of parametrized spatio-temporal fields

Computer Science > Machine Learning arXiv:2603.00290 (cs) [Submitted on 27 Feb 2026] Title:Scalable Gaussian process modeling of parametrized spatio-temporal fields Authors:Srinath Dama, Prasanth B. Nair View a PDF of the paper titled Scalable Gaussian process modeling of parametrized spatio-temporal fields, by Srinath Dama and 1 other authors View PDF HTML (experimental) Abstract:We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous representation, enabling predictions at arbitrary spatio-temporal coordinates, independent of the training data resolution. We leverage Kronecker matrix algebra to formulate a computationally efficient training procedure with complexity that scales nearly linearly with the total number of spatio-temporal grid points. A key feature of our approach is the efficient computation of the posterior variance at essentially the same computational cost as the posterior mean (exactly for Cartesian grids and via rigorous bounds for unstructured grids), thereby enabling scalable uncertainty quantification. Numerical studies on a range of benchmark problems demonstrate that the proposed method achieves accuracy competitive with operator learning methods such as Fourier neural operators and deep operator networks. On the one-dimensional unsteady Burgers' equation, our method surpasse...