The AFM-CG method produces anisotropic CG force fields from the FG many-body PMF by means of force and torque matching. In practice, identifying the CG potential U (R N , Ω N ) that yields CG forces and torques that satisfy the force-and torque-matching conditions in Eqs. ( ) and ( )-( ) exactly for any CG configuration (R N , Ω N ) is generally non-trivial. However, by approximating the CG potential U (R N , Ω N ; λ) as a set of functions that depends on a set of parameters λ, the optimal CG potential of this form subject to the force-and torque-matching conditions can be found as the one whose parameters λ minimize the average squared residual between the CG and FG forces and torques in corresponding system configurations, given by