A new methodology is presented for interfacing atomistic molecular dynamics simulations with continuum dynamics, and the approach is then applied to a model lipid bilayer system. The technique relies on a closed feedback loop in which atomistic level simulations are coupled with continuum level modeling. This approach allows for the examination of the trans-temporal and trans-spatial phenomena that occur in many biological systems, and nonequilibrium molecular dynamics are used to calculate the relevant transport coefficients that are required at the continuum level. It is found that for the membrane system there is significant information transfer across disparate spatial and temporal regimes, resulting in significant nonlinear behavior.