  Local causal states are latent representations that capture organized pattern
and structure in complex spatiotemporal systems. We expand their functionality,
framing them as spacetime autoencoders. Previously, they were only considered
as maps from observable spacetime fields to latent local causal state fields.
Here, we show that there is a stochastic decoding that maps back from the
latent fields to observable fields. Furthermore, their Markovian properties
define a stochastic dynamic in the latent space. Combined with stochastic
decoding, this gives a new method for forecasting spacetime fields.
