Simulation-based battery design encounters the difficulty of high computational cost. This paper presents a systematic approach based on the artificial neural network to reduce the computational burden of battery design by several orders-of-magnitude. Two neural networks are constructed using the finite element simulation results from a thermo-electrochemical model. The first neural network serves as a classifier to predict whether a set of input variables is physically feasible. The second neural network yields specific energy and specific power. Both neural networks are validated using extra finite element simulations out of the training data. With a global sensitivity analysis using the neural network, we quantify the effect of input variables on specific energy and specific power by evaluating large combinations of input variables, which is computationally prohibitive for finite element simulations. Among all parameters, the applied C-rate has the largest influence on specific power, while the electrode thickness and porosity are the dominant factors affecting specific energy. Based on this finding, we generate a design map that fulfills the requirements of both specific energy and specific power. Inparticular, we highlight the value of neural network in handling the non-linear, complex and computationally expensive problem of battery design and optimization.