A Nested Singular Value Decomposition-Based Surrogate Model for Spatiotemporal Flows

High-fidelity simulators serve as effective alternatives to physical experiments for understanding complex dynamics, which are often computationally expensive. While surrogate models enable rapid simulations, they typically fail to capture dynamic information from high-dimensional spatiotemporal flow fields. To address this, we propose a tailored multi-output Gaussian process (MOGP) surrogate model for spatiotemporal emulation, incorporating uncertainty quantification. Our approach leverages singular value decomposition to project high-dimensional spatiotemporal data into a low-dimensional latent space, with explicit analysis of decomposition errors. This reformulates the MOGP as a linear combination of independent Gaussian processes, each modeling the relationship between projection coefficients and simulator inputs. The resulting surrogate achieves reliable prediction of unobserved fluid dynamics while significantly accelerating computation, facilitating efficient design exploration. Validation through numerical experiments and real-data case studies demonstrates superior accuracy and efficiency over existing methods.