This approach is easily generalized to higher dimensions. The linearized TD-ADGA integral T mn I mn ℓ mn (lin.) is then calculated similar to Eq. 37 but where the multi-linear interpolation of the PES in the integration box is used instead of the global fitted PES for the MC. To test whether the linear approximation is good, the absolute difference between the TD-ADGA integral of the current iteration and the linearized TD-ADGA integral is compared to the linear threshold value ϵ lin . In effect, this condition ensures a minimum distance between the SPs that the TD-ADGA algorithm can place, because a linear approximation will be good for any potential PES if the grid becomes fine enough. We emphasize that the multi-linear interpolation is never used in the final PES representation and is solely used to identify domains of the PES where the representation is already good as interpolation between interval end points appears to be trivial.