AI 中文总结
研究利用物理信息神经网络求解非线性波动方程，将物理约束融入损失函数，无需标记数据。基于PINN的框架可对格罗斯-皮塔耶夫斯基方程和非线性薛定谔方程的孤子建模，预测解与解析结果吻合度高，能有效捕捉孤子轮廓，对相关研究有重要意义。
AI 中文摘要
本研究提出了一种数据驱动的框架，用于求解非线性波动方程，特别是格罗斯-皮塔耶夫斯基方程（GPE）和单分量非线性薛定谔方程（NLSE），采用物理信息神经网络（PINNs）。该方法将物理约束直接集成到神经网络的损失函数中，无需标记数据即可进行有效训练。实现了基于PINN的孤子框架，对两个方程的各种局域波结构进行建模。预测解与精确解析结果比较，误差小，吻合度高。该方法能有效捕捉GPE和NLSE中的孤子轮廓。框架的准确性和灵活性表明其对研究与玻色-爱因斯坦凝聚和非线性光学相关的非线性微分方程有用。
英文摘要
This study presents a data-driven framework for solving nonlinear wave equations, specifically the Gross-Pitaevskii equation (GPE) and the single-component nonlinear Schrodinger equation (NLSE), using Physics-Informed Neural Networks (PINNs). The approach integrates physical constraints directly into the neural network's loss function, enabling efficient training without requiring labelled data. We implement a PINN-based framework for solitons that models a variety of localized wave structures across both equations. Predicted solutions are compared with exact analytical results and show strong agreement with low error. The method effectively captures soliton profiles in both the GPE and NLSE. The accuracy and flexibility of the framework suggest its usefulness for studying nonlinear differential equations relevant to Bose--Einstein condensates and nonlinear optics.
Comments14 pages, 9 figures
Journal refPramana (Springer,July 2026)
