No, and I've looked. If you go to
Google Scholar and type in 'hugelkultur' you only get a handful of hits. If you type in "compost tea' though, you'll get over a thousand hits, this is a topic that is more amenable to scientific studies. If you enter "biochar" you get over 8000 hits.
I think the difficulty comes in defining hugelkultur so that you can do a controlled experiment. You could make mounds of different heights and study them, preferably over several growing seasons to see what happens over time, and have a control that was conventional agriculture. But I don't see studies like that being done and our Department of Agriculture doesn't seem to be funding proposals of that type.
If you were to propose a study of hugelkultur methods, just what factors would you study? The type of wood in the pile? The fungi it was inoculated with? The bacteria? The pH, osmotic pressure of water and air concentration in the hugelbed? The availability of N,P,K and other elements in the hugelbed soil? The way science is done is to identify cause and effect, hopefully one effect having one or at most a couple or three causes. Hugelkultur is all about creating a vibrant ecosystem of flora and fauna in one place and would be a nightmare to try and analyze by principle component regression.
That doesn't mean to say you can't be scientific about your approach to hugelkultur. You can include all sorts of things like biochar and
compost teas and companion planting and many other scientific principles in practicing hugelkultur, but when you compare your result to a conventional plot of a crop, to what do you attribute its effectiveness (or the lack of it)?
If you are still interested in digging through the scientific literature, I think you have to look past the word, and look for studies where soil organic carbon and the complexity of the soil food web are studied.