An exponential decay of a quantity \( g(x) \) is described by the equation
$$ \begin{equation} \tag{4} g'(x) = -\gamma g(x) \end{equation} $$with \( g(0) = g_0 \) for some chosen initial value \( g_0 \).
The analytical solution of (4) is
$$ \begin{equation} g(x) = g_0 \exp\left(-\gamma x\right) \tag{5} \end{equation} $$Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of (4).