Minor rewrite

We can thus set up a recurring series which depends on the inputs $x_i$ and $F_i$ and the previous values $h_{i-1}$. We assume now that the inputs at each step (or time $t_i$) is given by $x_i$ only and we denote the outputs for $\tilde{y}_i$ instead of $v_{i_1}$, we have then the compact equation for our outputs at each step $t_i$

We can think of this as an element in a recurrent network where our network (our model) produces an output $y_i$ which is then compared with a target value through a given cost/loss function that we optimize. The target values at a given step $t_i$ could be the results of a measurement or simply the analytical results of a differential equation.

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