<p>Modifying solution viscosity is a key functional application of polymers, yet the interplay of molecular chemistry, polymer architecture, and intermolecular interactions makes tailoring precise rheological responses challenging. We introduce a computational framework coupling topology-aware generative machine learning, Gaussian process modeling, and multiparticle collision dynamics to design polymers yielding prescribed shear-rate-dependent viscosity profiles. Targeting thirty rheological profiles of varying difficulty, Bayesian optimization identifies polymers that satisfy all low- and most medium-difficulty targets by modifying topology and solvophobicity, with other variables fixed. In these regimes, we find and explain design degeneracy, where distinct polymers produce near-identical rheological profiles. However, satisfying high-difficulty targets requires extrapolation beyond the initial constrained design space; this is rationally guided by physical scaling theories. This integrated framework establishes a data-driven yet mechanistic route to rational polymer design.</p>