  We propose a new technique to generate reasonable systems of partial
differential equations (PDE) that could be potential candidates for depicting
models in natural sciences related to quasi-linear equations. Such systems
appear within typical constructions of the Homological Algebra as complexes of
differential operators describing compatibility conditions for overdetermined
systems of PDE's. The related models can be both steady and evolutionary.
Additional assumptions on the ellipticity of the differential complex provide a
wide class of elliptic, parabolic and hyperbolic operators that could be
generated in this way. In particular, it appears that an essentially large
amount of equations related to the modern Mathematical Physics is generated by
the de Rham complex of differentials on the exterior differential forms. These
includes the elliptic Laplace and Lam\'e type operators; the parabolic heat
transfer equation; the Euler type and Navier-Stokes type equations in
Hydrodynamics; the hyperbolic wave equation and the Maxwell equations in
Electrodynamics; the Klein-Gordon equation in Relativistic Quantum Mechanics;
and so on. Our model generation method covers a broad class of generating
systems, especially in higher spatial dimensions, due to different basic
algebraic structures at play.
