Are there research based or scientific explanation on the working of Abhiññā / Iddhi? The following touches on the ability to know other people's thoughts at a much grosser level than developed through meditation: How we read each other's minds.

What are the research based or scientific explanation on the working of Abhiññā / Iddhi? What kind of cues do Jhāna help pick up?
Gathering of knowledge for attaining supernatural powers?

There has been a lot of research on this. During the '60's many universities in the US did various forms of paranormal research. Test subjects were collected and some filled with various kinds of experimental drugs to get results of different kinds. Some of these studies has been published for public viewing and some not. Also the Russians did research on this, but it is not known how far they got and nothing has ever been published. There are some rumors saying that they are still very active in this field.

There is an article on the subject here
http://www.oxfordbibliographies.com/view/document/obo-9780195393521/obo-9780195393521-0112.xml