  Estimating the rate of rare conformational changes in molecular systems is
one of the goals of Molecular Dynamics simulations. In the past decades, a lot
of progress has been done in data-based approaches towards this problem. In
contrast, model-based methods such as the Square Root Approximation (SqRA),
directly derive these quantities from the potential energy functions. In this
article we demonstrate how the SqRA formalism naturally blends with the tensor
structure obtained by coupling multiple systems, resulting in the tensor-based
Square Root Approximation (tSqRA). It enables efficient treatment of
high-dimensional systems using the SqRA and provides an algebraic expression of
the impact of coupling energies between molecular subsystems. Based on the
tSqRA, we also develop the Projected Rate Estimation (PRE), a hybrid
data-model-based algorithm that efficiently estimates the slowest rates for
coupled systems. In addition, we investigate the possibility of integrating
low-rank approximations within this framework to maximize the potential of the
tSqRA.
