Abstract The maximum achievable power of a polymer electrolyte membrane (PEM) fuel cell under specific operating temperature is important to its application. In this paper, we propose a method that integrates an artificial neural network (ANN) with the genetic algorithm (GA) to predict the performance of a PEM fuel cell and identify its maximum powers and corresponding conditions for operational control purpose. A validated three-dimensional (3D) multiphysics model is employed to generate total 1500 data points for training, testing, and verifying the ANN, which consists of two hidden layers with eight and four neurons on each hidden layer, respectively. After the ANN is properly trained, it is incorporated into the GA for deep learning to identify the maximum power and corresponding operating conditions, which shows that the fuel cell configuration could achieve a maximum power of about 0.78 W/cm2 at 368.8 K. Additionally, the combined ANN-GA method is employed to identify the maximum powers and their operating conditions under eight typical operation temperatures in the range of 323–373 K. The deep-learning results reflect the major physical and electrochemical processes that govern fuel cell performance and are validated against the 3D multiphysics model. The results demonstrate that the combined ANN-GA method is suitable to predicting fuel cell performance and identifying operation parameters for the maximum powers under various temperatures, which is important to practical system design and rapid control in fuel cell applications.