The structural features in silica aerogels are known to be modelled effectively by the diffusion-limited cluster-cluster aggregation (DLCA) approach. In this paper, an artificial neural network (ANN) is developed for predicting the fractal properties of silica aerogels, given the input parameters for a DLCA algorithm. This approach of machine learning substitutes the necessity of first generating the DLCA structures and then simulating and characterising their fractal properties. The developed ANN demonstrates the capability of predicting the fractal dimension for any given set of DLCA parameters within an accuracy of R2 = 0.973. Furthermore, the same ANN is subsequently inverted for predicting the input parameters for reconstructing a DLCA model network of silica aerogels, for a given desired target fractal dimension. There, it is shown that the fractal dimension is not a unique characteristic defining the network structure of silica aerogels, and the same fractal dimension can be obtained for different sets of DLCA input parameters. However, the problem of non-uniqueness is solved by using a guided gradient descent approach for predictive modelling purposes within certain bounds of the input parameter-space. Model DLCA structures are generated from the constrained and unconstrained inversion, and are compared against several parameters, amongst them, the pore-size distributions. The constrained inversion of the ANN is shown to predict the DLCA model parameters for a desired fractal dimension within an error of 2%.