DeepRV: Accelerating spatiotemporal inference with pre-trained neural priors

Gaussian Processes (GPs) provide a flexible and statistically principled foundation for modelling spatiotemporal phenomena, but their $\mathcal{O}(N^3)$ scaling makes them intractable for large datasets. Approximate methods such as variational inference (VI), inducing points (sparse GPs), low-rank factorizations (RFFs), local factorizations and approximations (INLA), improve scalability but trade off accuracy or flexibility. We introduce DeepRV, a neural-network surrogate that closely matches full GP accuracy including hyperparameter estimates, while reducing computational complexity to $\mathcal{O}(N^2)$, increasing scalability and inference speed. DeepRV serves as a drop-in replacement for GP prior realisations in e.g.~MCMC-based probabilistic programming pipelines, preserving full model flexibility. Across simulated benchmarks, non-separable spatiotemporal GPs, and a real-world application to education deprivation in London (n = 4,994 locations), DeepRV achieves the highest fidelity to exact GPs while substantially accelerating inference. Code is provided in the [anonymized] Python package, with all experiments run on single consumer-grade GPU to ensure accessibility for practitioners.