射线基函数神经网络用于在复合随机噪声下解决短暂概率密度函数
Zhengrong Jin1, Shuting Hou1, Hao Zhang2
1Northwestern Polytechnical University, School of Mathematics and Statistics, Xi'an 710072, China.
Physical review. E
|August 19, 2025
概括
一个新的辐射基功能神经网络 (RBF-NN) 准确地预测了系统在高斯和波桑白噪声与周期性激发相结合的情况下的反应. 这种深度学习方法为复杂的随机系统提供了卓越的效率和准确性.
科学领域:
- 随机系统分析 随机系统分析
- 计算物理 计算物理
- 应用数学 应用数学 应用数学
背景情况:
- 工程和科学系统通常会经历高斯白噪声,波桑白噪声和周期性激发的组合.
- 在这些复杂的条件下预测系统响应至关重要,但由于冲动跳跃和高频振荡,具有挑战性.
- 现有的方法很难有效,准确地处理这些不同类型噪音的综合影响.
研究的目的:
- 引入一种新的深度学习框架,即辐射基函数神经网络 (RBF-NN),用于分析具有合并随机和周期激发的系统.
- 为了准确地解决这些系统的短暂概率密度函数 (PDF) 中的高频振荡解决方案.
- 为了克服现有方法在处理高频组件的复合随机噪声方面的局限性.
主要方法:
- 开发了一个单层RBF-NN,具有均分布的神经元和RBF激活功能.
- 利用物理信息作为约束来解决管理瞬态PDF的前方科尔摩戈罗夫方程.
- 在积分计算中使用高斯-莱根德二次方程和在规范化约束中使用蒙特卡洛 (MC) 方法.
主要成果:
- 与标准的物理信息神经网络 (PINN) 和周期性PINN (P-PINN) 相比,RBF-NN框架显示了计算效率和准确性的显著改善.
- 该方法有效处理高频振荡溶液和复合随机噪声.
- 研究了神经元间距,形状参数,波桑噪声强度和周期性激发频率对RBF-NN性能的影响.
结论:
- 拟议的RBF-NN是一种高效和高效的方法,用于在复杂的噪声条件下解决前置科尔摩戈罗夫方程.
- 它将基于神经网络的方法的适用性扩展到更广泛的随机系统,特别是那些具有高频动态的系统.
- 在具有挑战性的工程和科学应用中,RBF-NN提供了一种可靠的解决方案,用于准确的响应预测.
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