  As a reduced representation of the nonlinear spectral fluxes of ideal
invariants in incompressible magnetohydrodynamics, we construct a
gradient-diffusion network model that combines phenomenological considerations
and geometrical analysis of the exact nonlinear energy transfer function. The
reduced-order representation of the conservative spectral transport of energy
and cross-helicity is of port-Hamiltonian form, which highlights the
flexibility and modularity of this approach. Numerical experiments with
Reynolds numbers up to $~10^6$ yield clear power-law signatures of
inertial-range energy spectra. Depending on the dominant timescale of energy
transfer, Kolmogorov (-5/3), weak-turbulence (-2), or Iroshnikov-Kraichnan-like
(-3/2) scaling exponents are observed. Anisotropic turbulence in a mean
magnetic field is successfully modelled as well. The characteristic exponents
of turbulence decay and the observed influence of cross-helicity on the energy
transfer are consistent with the literature and in agreement with theoretical
results.
