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 O(N3) scaling makes them intractable for large datasets. Approximate methods such as variational inference (VI), inducing-point (sparse) GPs, low-rank kernel approximations (e.g., Nystrom methods and random Fourier features), and approximations such as INLA improve scalability but typically trade off accuracy, calibration, or modelling flexibility. We introduce DeepRV, a neural-network surrogate that replaces GP prior sampling, while closely matching full GP accuracy at inference including hyperparameter estimates, and reducing computational complexity to O(N2), 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 dl4bi Python package, with all experiments run on a single consumer-grade GPU to ensure accessibility for practitioners.