  The quest to solve hard combinatorial optimization problems efficiently --
still a longstanding challenge for traditional digital computers -- has
inspired the exploration of many alternate computing models and platforms. As a
case in point, oscillator networks offer a potentially promising energy
efficient and scalable option. However, prior oscillator-based combinatorial
optimization solvers have primarily focused on quadratic combinatorial
optimization problems that consider only pairwise interaction among the
oscillators. In this work, we propose a new computational model based on the
maximum entropy production (MEP) principle that exploits higher order
interactions among the oscillators, and demonstrate its application in solving
the non-quadratic maximum satisfiability (MaxSAT) problem. We demonstrate that
the solution to the MaxSAT problem can be directly mapped to the entropy
production rate in the oscillator network, and subsequently, propose an
area-efficient hardware implementation that leverages Compute-in-Memory (CiM)
primitives. Using experiments along with analytical and circuit simulations, we
elucidate the performance of the proposed approach in computing high-quality
optimal / near-optimal solutions to the MaxSAT problem. Our work not only
reveals how oscillators can solve non-quadratic combinatorial optimization
problems such as MaxSAT but also extends the application of this dynamical
system-based approach to a broader class of problems that can be easily
decomposed to the MaxSAT solution.
