  This paper introduces multivariate input-output models to predict the errors
and bases dimensions of local parametric Proper Orthogonal Decomposition
reduced-order models. We refer to these multivariate mappings as the MP-LROM
models. We employ Gaussian Processes and Artificial Neural Networks to
construct approximations of these multivariate mappings. Numerical results with
a viscous Burgers model illustrate the performance and potential of the machine
learning based regression MP-LROM models to approximate the characteristics of
parametric local reduced-order models. The predicted reduced-order models
errors are compared against the multi-fidelity correction and reduced order
model error surrogates methods predictions, whereas the predicted reduced-order
dimensions are tested against the standard method based on the spectrum of
snapshots matrix. Since the MP-LROM models incorporate more features and
elements to construct the probabilistic mappings they achieve more accurate
results. However, for high-dimensional parametric spaces, the MP-LROM models
might suffer from the curse of dimensionality. Scalability challenges of
MP-LROM models and the feasible ways of addressing them are also discussed in
this study.
