基于物理学的神经网络,具有加权损失和强制约束,用于夸张的保存定律
Mahshid Sadat Ghoreishi1, Hamid Naderan2
1Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, 15916-34311, Iran.
Scientific reports
|January 6, 2026
概括
一种新的方法,加权损失硬约束物理信息神经网络 (WHC-PINN),准确地解决了过度方程,包括挑战流体流失连续性. 这个解决器有效地处理了里曼和喷嘴问题,为一般的可压缩流量模拟推进了PINNs.
科学领域:
- 计算流体动力学 计算流体动力学
- 科学机器学习科学机器学习
- 数字分析 数字分析
背景情况:
- 基于物理学的神经网络 (PINNs) 是解决微分方程的新兴工具.
- 解决流体流动中的冲击波等不连续性仍然是标准PINN的挑战.
- 欧勒方程对于模拟可压缩流体动力学,包括冲击波,至关重要.
研究的目的:
- 引入一种新的物理信息神经网络 (PINN) 方法,WHC-PINN,用于解决过度方程.
- 提高PINNs在处理可压缩流体流动中不连续性的能力.
- 开发一个统一的解决方案,用于里曼和合-分离喷嘴问题.
主要方法:
- 提出了一个加权损失硬约束物理信息神经网络 (WHC-PINN).
- 采用梯度权重方法和硬约束来解决过度方程.
- 使用欧勒方程验证WHC-PINN,专注于里曼和收-分离喷嘴问题.
主要成果:
- WHC-PINN成功地使用统一的保守配方解决了里曼和收-分离喷嘴问题.
- 解决者证明了解决初始值和边界值问题的能力.
- 与分析解决方案相比,WHC-PINN准确地捕获了冲击位置.
结论:
- WHC-PINN代表了在一般可压缩流量溶解器中使用PINN的重大进步.
- 拟议的方法有效地解决了不连续性,这是流体动力学模拟中的一个关键挑战.
- WHC-PINN为模拟复杂的流体流现象提供了强大而准确的方法.
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