I have a 1D problem as following
$$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x} \Big[ \frac{1}{2} \frac{\partial (g(x) f)}{\partial x} -\mu(x)f \Big]$$
I have a time-series of function $f$ already, for example, $\{f(x,t_i) \}_{i=0}^N$ for $t_0 <t<t_N$. My question is how to find $g(x)$ and $\mu(x)$. Both numerical and analytical answers are acceptable but numerical is preferred.
Thanks!