Channel charting is an unsupervised learning method that aims at mapping wireless channels to a so-called chart, preserving as much as possible spatial neighborhoods. In this paper, a model-based deep learning approach to this problem is proposed. It builds on a physically motivated distance measure to structure and initialize a neural network that is subsequently trained using a triplet loss function. The proposed structure exhibits a low number of parameters and clever initialization leads to fast training. These two features make the proposed approach amenable to on-the-fly channel charting. The method is empirically assessed on realistic synthetic channels, yielding encouraging results.