Aiming at the problem that traditional inversion methods excessively rely on the initial model, resulting in unstable results and low computational efficiency, a real-time inversion method for logging while drilling (LWD) is proposed by integrating independent recurrent neural network and particle swarm optimization algorithm. First, an independent recurrent neural network model is built from sequence data generated by stratigraphic forward modeling, and an attention mechanism is introduced to emphasize the role of key features in the LWD inversion. Next, stochastic inertia weights are introduced into a particle swarm optimization algorithm to improve its global and local search capabilities, and hyperparameter-optimization of neural network model is carried out using the particle swarm optimization algorithm. Finally, ablation experiments and comparison experiments are conducted on the test set of forward simulation and the test set of logging data from 1931–2132 m section of an oil field respectively. The results prove that the particle swarm algorithm and the attention mechanism can effectively improve the prediction accuracy, and the inversion performance of this method is superior to that of the long short-term memory (LSTM) networks, the bi-directional LSTM networks, and the gated recurrent unit (GRU) networks in all aspects, meeting the needs of the real-time inversion of LWD data.