Is there a classification of differential equations over the field of fractions of formal power series? (characteristic 0)

Question

Let $k$ be an algebraically closed field of characteristic 0. Consider the field of fractions of formal power series $K:= Frac(k[[T_1,...,T_n]])$. We have the corresponding algebra of differential operators $D = K[\partial_1,\partial_2,...,\partial_n]$ with $[\partial_i,f]= \partial_i f$.

Is there a classification of finitely generated modules over $D$ for $n>1$?