The paper proposes Galerkin-like projection method which preserves dilation symmetries of linear and nonlinear (possibly unbounded) operators. The method is developed for approximation of generalized homogeneous evolution equations in Hilbert spaces. It is shown that the obtained reduced-order model preserve stability and convergence properties (such as finite-time and fixed-time stability) of the original system. The proposed method is compared on simulations with the classical Galerkin method for the Burgers equation. Key word. approximation of distributed parameter systems; semigroup and operator theory.