Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents significant challenges due to the complexity of the underlying equations and the computational resources required for accurate solutions. To address this, we have developed a novel method using neural network (NN) to efficiently solve solitons. A similar NN approach is Physics-Informed Neural Networks (PINN). In a comparative analysis between our method and PINN, we find that our method achieves shorter computation times while maintaining the same level of accuracy. This advancement in computational efficiency not only overcomes current limitations but also opens new avenues for studying topological solitons and their dynamical behavior.

翻译：拓扑孤子作为非线性微分方程的稳定局域解，在粒子物理学和宇宙学等物理学与数学的多个领域中具有关键意义。然而，由于基础方程的复杂性以及精确求解所需的计算资源，求解这些孤子面临着重大挑战。为此，我们开发了一种利用神经网络（NN）高效求解孤子的新方法。一种类似的神经网络方法是物理信息神经网络（PINN）。在我们的方法与PINN的比较分析中，我们发现我们的方法在保持相同精度水平的同时实现了更短的计算时间。这一计算效率的提升不仅克服了当前的局限性，还为研究拓扑孤子及其动力学行为开辟了新途径。