Predicting the fold of a protein from its amino acid sequence is one of the grand problems in computational biology. While there has been progress towards a solution, especially when a protein can be modelled based on one or more known structures (templates), in the absence of templates, even the best predictions are generally much less reliable. In this paper, we present an approach for predicting the three-dimensional structure of a protein from the sequence alone, when templates of known structure are not available. This approach relies on a simple reconstruction procedure guided by a novel knowledge-based evaluation function implemented as a class of artificial neural networks that we have designed: Neural Network Pairwise Interaction Fields (NNPIF). This evaluation function takes into account the contextual information for each residue and is trained to identify native-like conformations from non-native-like ones by using large sets of decoys as a training set. The training set is generated and then iteratively expanded during successive folding simulations. As NNPIF are fast at evaluating conformations, thousands of models can be processed in a short amount of time, and clustering techniques can be adopted for model selection. Although the results we present here are very preliminary, we consider them to be promising, with predictions being generated at state-of-the-art levels in some of the cases.