基于（量子）神经网络的多非线性波：检验AI的优越性
Multiple Nonlinear Waves by (Quantum) Neural Networks: Checking the AI supremacy
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中文总结 AI 辅助
本研究通过数值实验与性能指标，检验量子物理信息神经网络（QPINN）求解带周期边界条件的Korteweg-de Vries方程描述的弱非线性介质多波传播问题的适用性，测试其在该场景下的应用成熟度。
中文摘要 AI 辅助
为测试所谓的量子物理信息神经网络（QPINN）技术求解演化偏微分方程的潜力，我们考虑由带周期边界条件的Korteweg-de Vries方程描述的弱非线性介质中多波传播问题。尽管该问题可解析求解，但高亏格解对数值方法而言是极具挑战性的测试平台。因此，我们的思路是通过提供一组性能指标并开展多项数值实验，检验QPINN在该场景下应用是否足够成熟。
英文摘要
To test the potential of so-called quantum physics-informed neural network (QPINN) technology for solving evolutionary partial differential equations, we consider the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions. Although this problem is solvable analytically, high-genus solutions could represent a rather challenging testbed for numerical methods. Therefore, our idea is to test whether a QPINN is sufficiently mature for application in this context by providing a set of indicators of merit and performing several numerical experiments.
发表机构
- Università del Salento（萨伦托大学）
- INFN, Sezione di Lecce（意大利国家核物理研究所莱切分部）
- IIT Lecce（意大利理工学院莱切分部）
机构由 AI 辅助整理，请以论文原文为准。
