In this paper, multiple rogue wave solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation were studied by applying the bilinear neural network method. First, we introduced a single-hidden layer neural network model (NMM) and several types of solutions which can be calculated by this model have been summarized. Additionally, we introduced a “3-2-4” NNM and obtained the solution expression by choosing particular weight coefficients and test functions of the model. Then, through different center of this model, we gave three kinds of rogue wave solutions centered at the origin and three kinds of rogue wave solutions centered with a fixed center. The solutions centered with a fixed center were studied in detail. Finally, several groups of images with physical interpretation, including three-dimensional, contour and density plots exhibited their dynamic structure and physical properties. Furthermore, the obtained results have immensely augmented the exact solutions of the (2+1)-dimensional Sharma–Tasso–Olver equation on the existing literature and enabled us to understand the nonlinear dynamic system deeply, and thus, the proposed method will be a strong boost to the calculation method of nonlinear equations.

本文应用双线性神经网络方法研究了(2+1)维Sharma-Tasso-Olver方程的多重流氓波解。首先，我们介绍了一个单隐藏层神经网络模型（NMM），并总结了可以通过该模型计算的几种类型的解决方案。此外，我们引入了“3-2-4”NNM，并通过选择模型的特定权重系数和测试函数来获得解表达式。然后，通过该模型的不同中心，我们给出了三种以原点为中心的流氓波解和三种以固定中心为中心的流氓波解。详细研究了以固定中心为中心的解决方案。最后，几组具有物理解释的图像，包括三维，等高线和密度图展示了它们的动态结构和物理特性。此外，所获得的结果极大地扩充了现有文献中 (2+1) 维 Sharma-Tasso-Olver 方程的精确解，使我们能够深入了解非线性动力系统，因此，所提出的方法将是一个对非线性方程的计算方法有很大的推动作用。