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Based on conservation laws as one of the important integrable properties ofnonlinear physical models, we design a modified physics-informed neural networkmethod based on the conservation law constraint. From a global perspective,this method imposes physical constraints on the solution of nonlinear physicalmodels by introducing the conservation law into the mean square error of theloss function to train the neural network. Using this method, we mainly studythe standard nonlinear Schr\"odinger equation and predict various data-drivenoptical soliton solutions, including one-soliton, soliton molecules,two-soliton interaction, and rogue wave. In addition, based on various exactsolutions, we use the modified physics-informed neural network method based onthe conservation law constraint to predict the dispersion and nonlinearcoefficients of the standard nonlinear Schr\"odinger equation. Compared withthe traditional physics-informed neural network method, the modified method cansignificantly improve the calculation accuracy.

Modified physics-informed neural network method based on the conservation law constraint and its prediction of optical solitons