Figure 1.

The workflow and the framework of the neural information squeezer. $x_t$ is the data at time t. Encoder ${\psi }_{\alpha }$ is an invertible neural network (INN), from which the coarse-grained data $y_t$ can be generated. The dynamics learner $f_{\beta }$ is a common feed-forward neural network with parameters $\beta$ . Through it the evolution from $y_t$ to $y(t+1)$ can be conducted. The decoder converts the predicted macro-state of the next time step $\mathbf{y}(t+1)$ into the prediction of the micro-state at the next time step ${\widehat{\mathbf{x}}}_{t+1}$ .