Neural Simulation-Based Inference for space-time Gaussian processes
Abstract
In spatio-temporal data analysis, estimating covariance parameters for Gaussian random fields via maximum likelihood estimation (MLE) is computationally prohibitive for large datasets. Following recent advances in simulation-based inference techniques, we propose two neural network architectures — Neural Bayes Estimation (NBE) and Neural Ratio Estimation (NRE) — to learn the parameters of Gaussian spatio-temporal Gneiting-Matérn models with advection. The networks are trained on simulations generated directly from the underlying Gaussian random field model. A thorough simulation study demonstrates strong performance across one-dimensional time and both one-dimensional space and two-dimensional space, yielding high accuracy and reliable uncertainty quantification for both NBE and NRE. Through extensive offline training, the framework achieves fully amortized inference, replacing costly optimization with a single forward pass. Finally, we apply our framework to solar radiation prediction and short-term forecasting. By adopting a sliding-window approach, the model accounts for temporal non-stationarity while retaining this key advantage: achieving near-instantaneous parameter inference and forecasting.
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BibTeX
@misc{loret2026neural,
title = {{Neural Simulation-Based Inference for space-time Gaussian processes}},
author = {Alexandre Loret and Lucia Clarotto and Nicolas Desassis and Thomas Romary},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36855},
eprint = {2610.36855},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05646982v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Neural Simulation-Based Inference for space-time Gaussian processes
AU - Alexandre Loret
AU - Lucia Clarotto
AU - Nicolas Desassis
AU - Thomas Romary
PY - 2026
DA - 2026/10/24
PB - HAL
DO - 10.48550/arxiv.2610.36855
UR - https://hal.science/hal-05646982v1
AB - In spatio-temporal data analysis, estimating covariance parameters for Gaussian random fields via maximum likelihood estimation (MLE) is computationally prohibitive for large datasets. Following recent advances in simulation-based inference techniques, we propose two neural network architectures — Neural Bayes Estimation (NBE) and Neural Ratio Estimation (NRE) — to learn the parameters of Gaussian spatio-temporal Gneiting-Matérn models with advection. The networks are trained on simulations generated directly from the underlying Gaussian random field model. A thorough simulation study demonstrates strong performance across one-dimensional time and both one-dimensional space and two-dimensional space, yielding high accuracy and reliable uncertainty quantification for both NBE and NRE. Through extensive offline training, the framework achieves fully amortized inference, replacing costly optimization with a single forward pass. Finally, we apply our framework to solar radiation prediction and short-term forecasting. By adopting a sliding-window approach, the model accounts for temporal non-stationarity while retaining this key advantage: achieving near-instantaneous parameter inference and forecasting.
ER -