  Field-scale properties of fractured rocks play crucial role in many
subsurface applications, yet methodologies for identification of the
statistical parameters of a discrete fracture network (DFN) are scarce. We
present an inversion technique to infer two such parameters, fracture density
and fractal dimension, from cross-borehole thermal experiments data. It is
based on a particle-based heat-transfer model, whose evaluation is accelerated
with a deep neural network (DNN) surrogate that is integrated into a grid
search. The DNN is trained on a small number of heat-transfer model runs, and
predicts the cumulative density function of the thermal field. The latter is
used to compute fine posterior distributions of the (to-be-estimated)
parameters. Our synthetic experiments reveal that fracture density is well
constrained by data, while fractal dimension is harder to determine. Adding
non-uniform prior information related to the DFN connectivity improves the
inference of this parameter.
