Autonomic closure is a new technique for achieving physically accurate adaptive closure of coarse-grained turbulent flow governing equations, such as those solved in large eddy simulations (LES). Although autonomic closure has been shown in recent a priori tests to more accurately represent unclosed terms than do dynamic versions of traditional LES models, the optimization step used in the approach introduces large matrices that must be inverted, resulting in high memory usage. In order to reduce memory requirements, here we propose the use of approximate Bayesian computation (ABC) in place of the optimization step, thereby yielding an autonomic closure implementation that trades memory-intensive for processor-intensive computations. These computations can be handled by co-processors such as general purpose graphical processing units that are becoming increasingly available on petascale supercomputers. In this paper, we outline the formulation of ABC-enabled autonomic closure and present initial results demonstrating the accuracy of the approach.