In this study,we implement forward modeling and inversion based on deep-learning strategies using an optimal nearly analytic discrete(ONAD)method.The forward-modeling method combines the ONAD method with recurrent neural network(RNN)for the first time.RNN is a type of neural network that is suitable for sequential data,which uses information from both previous and current times to obtain output information.We express the ONAD method using an RNN framework to advance the time iteration of an acoustic equation.This process can simplify programming using RNN and convolution kernels.Next,we use deep learning based on the proposed forward-modeling method to study full waveform-inversion problems.Because the main purpose of inversion is to minimize the error between real and synthetic data,inversion is essentially an optimization problem.Many new optimizers are available in the framework of deep learning,such as the Adam and Nadam optimizers,which are used for optimizing velocity model in the inversion process.We perform six numerical experiments.The first two experiments demonstrate the forward-modeling results,which indicate that the forward-modeling method can effectively suppress numerical dispersion and improve computational efficiency.The other four experiments demonstrate the inversion results,which show that the method proposed in this paper can effectively realize inversion imaging.We compare several optimizers used in deep learning and find that the Nadam optimizer has faster convergence and better effectiveness based on the ONAD method combined with RNN.