The network {NN}_{dyn} receives the input u ( t ) and the latent state s ( t ) and returns the time derivative of the latent state, thus defining its dynamics. The network {NN}_{rec} , instead, is evaluated only when an estimate of the output field y is sought. More precisely, an approximation of y ( x , t ) is recovered by giving as an input to {NN}_{rec} the latent state at time t and the query space coordinate x Ω. In general, the reconstruction network {NN}_{rec} might take as an input u ( t ) as well (see e.g. Results, Test Case 2); for simplicity, in the figure we represent the special case when {NN}_{rec} does not depend on u ( t ).
