用神经网络高效求解拓扑孤子，速度更快精度相当。
Comparative Study of Neural Network Methods for Solving Topological Solitons
- 自研神经网络方法替代传统求解方式
- 计算时间显著缩短，精度与PINN持平
- 适合需快速模拟孤子行为的研究者
拓扑孤子是非线性微分方程的稳定局域解，在粒子物理和宇宙学等领域具有重要意义。然而，由于方程复杂且对计算资源要求高，求解困难。本文提出一种新型神经网络方法，用于高效求解孤子；与物理信息神经网络（PINN）进行对比分析发现，该方法在保持相同精度的前提下，显著缩短了计算时间。这一计算效率的提升不仅突破了现有瓶颈，也为研究拓扑孤子及其动态行为开辟了新路径。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。