"understand on the basis of" is correct and usable in written English.
You can use this phrase to indicate that you understand something, but your understanding is based on something else. For example, "I understand on the basis of your explanation why this problem occurs."
Politics requires a coming together of people of different fundamental convictions to formulate and justify policy in terms that all understand, on the basis of principles that as many as possible can share.
Further, some variability in the reporting of risks seems hard to understand on the basis of local concern, considering subject protection and information are key goals of all REBs and research ethics policy and that the basic risks of MRI and fMRI do not vary in essence between sites.
In both cases, our understanding of the parts hinges on our understanding of a larger whole, which, again, can only be understood on the basis of the parts.
Mr Shamdasani claims that eventually all Jung's work will be understood on the basis of this book and that previous writing about him will have to be revised.
This can be understood on the basis of density of defect states.
Every carefully observed face is understood on the basis of such a dominant impression ….
Solubility profiles were understood on the basis of structural and solvent solute interaction approaches.
Competing demands can be understood on the basis of how their inherent features are constituted in practice.
The contemporary laws of constant and multiple proportions deal with a concept of elemental proportions understood on the basis of the concept of mass.
This is understood on the basis of the yttrium-doping-induced structural defect effects in the passive films.
Most of the underlying laws behind such occurrences can only be understood on the basis of the theory of Markov chains.
