Multiscale modeling is a class of methods that solve physical problems by considering 
essential physics at multiple spatial and temporal scales. Many biological processes 
involve key phenomena at distinct scales and understanding of those systems requires 
effective multiscale analyses by linking important features across molecular, cellular, 
tissue and organ levels. In the first part of this talk, a multi-scale homogenization of 
DNA molecules is presentned. A wavelet projection method is first introduced to form a 
coarse-grained DNA molecule represented with superatoms. The coarsened MD model offers a 
simplified molecular structure for the continuum description of DNA molecules. In the 
second half of the presentation, a radial basis (RF) representation of molecular dynamics 
(MD) force fields is proposed for proper orthogonal decomposition (POD) based reduced-
order modeling of the molecular dynamics system. The MD potential functions and inter-
atomic forces are approximated by the radial basis functions (RBFs) in the generalized 
reduced-order space. With the construction of the RBF approximated force fields, the 
inter-atomic forces and the reduced-order MD model can be effectively formulated in the 
reduce-order coordinates in which the reduced-order MD model is constructed. The numerical 
study shows that the proposed POD-based model order reduction approach maintains the 
similar level of accuracy to the conventional MOR technique whereas computational 
efficiency is considerably enhanced.