| Summary: | Abstract To enhance the precision and efficiency of result prediction, we proposed a parallel hard-constraint physics-informed neural networks (phPINN) by combining the parallel fully-connected neural network structure and the residual-based adaptive refinement method. We discussed the forward and inverse problems of the nonlinear Schrödinger–Maxwell–Bloch equation via the phPINN. In the forward problem, we predict five forms of soliton solutions and rogue wave dynamics under corresponding initial and boundary conditions; In the inverse problem, we predict the equation parameter using the training data with different noise intensities, initial values, and solution forms. The predicted parameters achieve a relative error of less than 1%. These results validate the effectiveness of the phPINN algorithm in solving forward and inverse problems of three-component coupled equations.
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