Experimental polarising microscopy texture images of the fluid smectic phases and sub-phases of the classic liquid crystal MHPOBC were classified as paraelectric (SmA*), ferroelectric (SmC*), ferrielectric (SmC1/3*), and antiferroelectric (SmCA*) using convolutional neural networks, CNNs. Two neural network architectures were tested, a sequential convolutional neural network with varying numbers of layers and a simplified inception model with varying number of inception blocks. Both models are successful in binary classifications between different phases as well as classification between all four phases. Optimised architectures for the multi-phase classification achieved accuracies of (84 ± 2)% and (93 ± 1)% for sequential convolutional and inception networks, respectively. The results of this study contribute to the understanding of how CNNs may be used in classifying liquid crystal phases. Especially the inception model is of sufficient accuracy to allow automated characterization of liquid crystal phase sequences and thus opens a path towards an additional method to determine the phases of novel liquid crystals for applications in electro-optics, photonics or sensors. The outlined procedure of supervised machine learning can be applied to practically all liquid crystal phases and materials, provided the infrastructure of training data and computational power is provided.