  The intrinsic energy minimization in dynamical systems offers a valuable tool
for minimizing the objective functions of computationally challenging problems
in combinatorial optimization. However, most prior works have focused on
mapping such dynamics to combinatorial optimization problems whose objective
functions have quadratic degree (e.g., MaxCut); such problems can be
represented and analyzed using graphs. However, the work on developing such
models for problems that need objective functions with degree greater than two,
and subsequently, entail the use of hypergraph data structures, is relatively
sparse. In this work, we develop dynamical system-inspired computational models
for several such problems. Specifically, we define the 'energy function' for
hypergraph-based combinatorial problems ranging from Boolean SAT and its
variants to integer factorization, and subsequently, define the resulting
system dynamics. We also show that the design approach is applicable to
optimization problems with quadratic degree, and use it develop a new dynamical
system formulation for minimizing the Ising Hamiltonian. Our work not only
expands on the scope of problems that can be directly mapped to, and solved
using physics-inspired models, but also creates new opportunities to design
high-performance accelerators for solving combinatorial optimization.
