This paper investigates intelligent reconfigurable surface-assisted non-orthogonal multiple access (NOMA) networks for short packet communications where the source with multiple antennas utilizes beamforming technology to serve two end users including a near user and a far user. The analysis system, closed-form expressions of the average block error rates (BLERS), latency and reliability at all users are derived under assuming perfect channel state information over quasi-static Rayleigh fading channels. For evaluating the improvement of the network system, a deep neural network (DNN) framework is designed to predict the performance parameters in two cases: (i) BLERS prediction of the users, (ii) transmit power allocation under the constraints of BLERS at each user which satisfy the extremely high reliability requirements of uRLLCs. The extensive results demonstrate that first, the DNN-based estimation results are more accurate than Monte-Carlo simulation results with low execution time. Second, the allocated power for each user can be accurately predicted at the high layers. Finally, two methods of evaluating the effectiveness of the DNN model, i.e. root mean square error and mean absolute percentage error, reach low error which verify the power of the designed DNN model for future analysis