物理编码神经网络的应用,以提高复杂的多尺度系统属性的可预测性
Marcel B J Meinders1,2, Jack Yang3,4, Erik van der Linden3,4
1Wageningen University and Research Centre, Wageningen, The Netherlands. marcel.meinders@wur.nl.
Scientific reports
|July 1, 2024
概括
基于物理学的神经网络 (PINNs) 在预测乳液粘度方面优于标准的神经网络 (NNs). PINN准确地捕捉复杂的系统属性,特别是在数据有限的情况下.
科学领域:
- 计算物理学的计算物理.
- 材料科学是一种材料科学.
- 化学工程是化学工程的组成部分.
背景情况:
- 预测复杂的多尺度系统的物理性质是具有挑战性的,因为基于物理的模型和数据可用性的局限性.
- 机器学习 (ML) 提供了潜在的解决方案,但通常需要大量的数据集.
- 结合物理和机器学习的混合方法可以解决这些挑战.
研究的目的:
- 评估基于物理学的神经网络 (PINNs) 与用于预测乳液粘度的标准神经网络 (NNs) 的性能.
- 调查超参数对NN和PINN模型性能的影响.
- 评估PINNs处理外推和插值任务的能力.
主要方法:
- 开发和应用标准神经网络 (NN) 和基于物理学的神经网络 (PINN).
- 训练和测试模型以预测乳液粘度作为剪切速率的函数.
- 使用性能指标,如平均平方误差和确定系数.
- 使用弗里德曼测试进行统计验证.
主要成果:
- 在所有绩效指标上,PINN的表现始终优于NN.
- 在统计学上,PINNs的优异性能是显著的 (p < 0.0002).
- 与标准的NNs不同,PINNs表现出强大的外推和插值能力.
- 网络超参数和优化方法没有影响这些发现.
结论:
- 将物理信息编码到神经网络 (PINNs) 中可以显著提高复杂系统的预测准确性.
- 当处理有限的数据集时,PINNs特别有利.
- 这种方法提供了一种可扩展和有前途的方法,通过整合特定领域的知识来预测复杂系统的特性.
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