In this work we present a sparse approximate Bayesian inference method for model inversion of partial differential equation (PDE) models with heterogeneous parameters. In our approach we construct a probabilistic representation of model parameters in terms of "pilot" values of said parameters evaluated at a finite set of "pilot" points. Inference is performed via variational inference algorithms for empirical Bayes. The proposed method provides an accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation for model inversion.