Evaluation of CG forces and torques from the expression for the CG potential in Eq. ( ) can be computationally costly if the number of basis functions is large. To expedite force and torque evaluations so as to enable more efficient CG MD simulations, we have fit the optimized CG potential obtained by AFM-CG to a simpler analytical form containing a smaller number of parameters. The reason for first optimizing the parameters in the CG potential given by a linear basis-set expansion by force-and torque-matching instead of directly doing force-and torque-matching on this simpler nonlinear function is that optimization can be achieved efficiently with the linear function in a single step by solving a matrix equation, instead of requiring a multi-step iterative process. Alternatively, optimization of a CG potential that is a nonlinear function of its parameters by force-and torque-matching could be achieved directly by, for example, adapting previous approaches for optimizing nonlinear CG potentials to minimize an objective function. To obtain the parameters for the simpler potential, we minimized the difference between this potential and the CG potential given by the linear basis-set expansion for a large number of pair configurations from the FG simulations that were used for CG parametrization. The Trust Region Reflective nonlinear least-squares algorithm 46 in the optimize.least squares module of the SciPy python package was used for this purpose. For this simpler potential, we have used a modified form of the S-function potential U S for disk-shaped particles, to which two additional terms, U exp and U osc , have been added to enable a better fit to the CG potential: U exp enables a better fit to the repulsive part of the potential, while U osc captures oscillations in the potential. Thus, the pair-wise potential between uniaxial CG particles I and J, which is a function of the vector R IJ = R I -R J that connects the particle centers and the unit vectors ûI and ûJ along the unique axis of each particle, was fitted to the form