在物理信息的神经网络中,损失驱动的动态重量和残余转换
Yabin Zhang1, Liang-Jian Deng2
1organization=School of Mathematical Sciences, University of Electronic Science and Technology of China, city=Chengdu, Sichuan, postcode=611731, country=China.
概括
物理信息神经网络 (PINNs) 显示损失功能失衡. 一个新的动态重量PINN和残余转换PINN (ResTranPINN) 提高了解决部分微分方程 (PDE) 的准确性和效率.
科学领域:
- 计算物理学的计算物理.
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 物理信息神经网络 (PINNs) 越来越多地用于由部分微分方程 (PDEs) 控制的前向和反向问题.
- 在PINN培训中,一个关键的挑战是经验风险损失函数中的不平衡,阻碍了最佳表现.
- 了解PINN故障模式,特别是在高维反向问题中,对于可靠的科学发现至关重要.
研究的目的:
- 识别和解决PINN中的损失函数不平衡.
- 开发新的PINN方法,以提高准确性和计算效率.
- 为复杂的PDEs提供PINN优化和故障机制的理论见解.
主要方法:
- 引入一个损失驱动的动态重量PINN,并使用神经触点内核进行理论分析.
- 对复杂的,依赖时间的物理现象进行全面评估,并采用各种学习速度衰减策略.
- 开发了基于限制等价性的残余转换PINN (ResTranPINN) 算法,以实现加速趋同.
主要成果:
- 在各种物理问题上证明了动态重量PINN的有效性.
- 量化了动态权重更新频率和分配对准确性和效率的影响.
- ResTranPINN算法显著加快了融合,并减少了逆向问题的计算时间.
结论:
- 拟议的动态重量和ResTranPINN方法为PINN培训挑战提供了强大的解决方案.
- 这些进步提供了对PINN优化和故障模式的更深入理解.
- 该研究建立了一个全面的框架,以提高PINNs在科学应用中的可靠性和效率.
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