  Stochastic generators are essential to produce synthetic realizations that
preserve target statistical properties. We propose GenFormer, a stochastic
generator for spatio-temporal multivariate stochastic processes. It is
constructed using a Transformer-based deep learning model that learns a mapping
between a Markov state sequence and time series values. The synthetic data
generated by the GenFormer model preserves the target marginal distributions
and approximately captures other desired statistical properties even in
challenging applications involving a large number of spatial locations and a
long simulation horizon. The GenFormer model is applied to simulate synthetic
wind speed data at various stations in Florida to calculate exceedance
probabilities for risk management.
