AW-EL-PINNs:在最佳控制问题上的欧勒-拉格朗日系统的多任务学习物理信息的神经网络
1College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China.
概括
本研究引入了适应加权欧勒-拉格朗日定理结合物理信息的神经网络 (AW-EL-PINNs) 以实现最佳控制. 与传统方法相比,AW-EL-PINNs可以提高欧勒-拉格朗系统的解决方案精度和稳定性.
科学领域:
- 计算数学 计算数学 计算数学
- 机器学习 机器学习
- 最佳控制理论 最佳控制理论
背景情况:
- 欧勒-拉格朗日系统是经典力学和最佳控制的基础.
- 解决这些系统通常涉及复杂的数值方法和手动参数调.
- 现有的物理信息神经网络 (PINNs) 需要大量的努力来平衡损失的功能.
研究的目的:
- 为了提出一个新的框架,自适应加权欧勒-拉格朗日定理结合了物理信息的神经网络 (AW-EL-PINNs),用于在最佳控制下解决欧勒-拉格朗日系统.
- 提高解决最佳控制问题的效率和准确性.
- 在深度学习方法中减少对损失函数权重的手动调整的需求.
主要方法:
- 拟议的AW-EL-PINNs框架将欧勒-拉格朗日定理与深度学习架构集成在一起.
- 最佳控制问题系统地转化为两点边界值问题 (TPBVPs).
- 适应性损失权衡机制在训练期间动态平衡损失组件,减少手动干预.
主要成果:
- 在五个数值示例中,AW-EL-PINNs显示了增强的解决方案准确性.
- 在整个优化过程中,框架保持了稳定性.
- 在精度和稳定性方面,性能优于基线方法.
结论:
- AW-EL-PINNs提供了一种强大而准确的方法,用于在最佳控制下解决欧勒-拉格朗系统.
- 通过减少手动调整,自适应性损失权衡机制显著改善了传统PINNs.
- 这种框架对各种物理系统中的应用具有前景,需要精确的最佳控制解决方案.
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