Parametric dynamical systems pose significant challenges for projection-based model reduction due to the nonlinear, and often nonsmooth, dependence of solutions on parameters. Well-studied approximations based on the Proper Orthogonal Decomposition (POD), while cheap to compute and highly robust to their inputs, are also data hungry and agnostic to parametric variation due to their use of a global linear function space. The present talk considers alternative reduced-order models (ROMs) based on the multilinear Tucker decomposition, which offers a path around these issues by nonlinearly tailoring their reduced basis to each parameter instance via the interpolation of factorized tensor snapshots. Extending ideas from [1] to incorporate energy conservation in weighted inner product spaces, we show that such ROMs can be effective on a variety of interesting test cases, including wave-type phenomena exhibiting Hamiltonian structure. A novel interpolation procedure based on radial basis functions further improves data efficiency, suggesting the proposed ROMs as effective surrogates for certain classes of advection-dominated systems.