The use of solid oxide fuel cells (SOFCs) is a promising approach towards achieving sustainable electricity production from fuel. The utilisation of the hydrocarbons and biomass in SOFCs is particularly attractive owing to their wide distribution, high energy density, and low price. The long-term operation of SOFCs using such fuels remains difficult owing to a lack of an effective diagnosis and optimisation system, which requires not only a precise analysis but also a fast response. In this study, we developed a hybrid model for an on-line analysis of SOFCs at the cell level. The model combines a multi-physics simulation (MPS) and deep learning, overcoming the complexity of MPS for a model-based control system, and reducing the cost of building a database (compared with the experiments) for the training of a deep neural network. The maximum temperature gradient and heat generation are two target parameters for an efficient operation of SOFCs. The results show that a precise prediction can be achieved from a trained AI algorithm, in which the relative error between the MPS and AI models is less than 1%. Moreover, an online optimisation is realised using a genetic algorithm, achieving the maximum power density within the limitations of the temperature gradient and operating conditions. This method can also be applied to the prediction and optimisation of other non-liner, dynamic systems.