The MUI library is a collaborative development between Brown University, Lawrence Berkeley National Laboratory, UK Research & Innovation Science & Technology Facilities Council and IBM Research.

MUI was originally developed by the CRUNCH group within the Division of Applied Mathematics at Brown University and described in their 2015 paper, Multiscale Universal Interface: A Concurrent Framework for Coupling Heterogeneous Solvers. More recently developers from the other institutions in the consortium have joined in to help evolve and improve MUI by applying it to new and challenging coupled problems.