  In this paper, we investigate finite representations of DatalogMTL models.
First, we discuss sufficient conditions for detecting programs that have finite
models. Then, we study infinite models that eventually become constant and
introduce sufficient criteria for programs that allow for such representation.
We proceed by considering infinite models that are eventually periodic and show
that such representation encompasses all DatalogMTL^FP programs, a widely
discussed fragment. Finally, we provide a novel algorithm for reasoning over
such finite representable programs.
