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Abstract：
Predicting physical properties of complex multi-scale systems is a common challenge and demands analysis of various temporal and spatial scales. However, physics alone is often not sufficient due to lack of knowledge on certain details of the system. With sufficient data, however, machine learning techniques may aid. If data are yet relatively cumbersome to obtain, hybrid methods may come to the rescue. We focus in this report on using various types of neural networks (NN) including NN\'s into which physics information is encoded (PeNN\'s) and also studied effects of NN\'s hyperparameters. We apply the networks to predict the viscosity of an emulsion as a function of shear rate. We show that using various network performance metrics as the mean squared error and the coefficient of determination ( R 2 ) that the PeNN\'s always perform better than the NN\'s, as also confirmed by a Friedman test with a p-value smaller than 0.0002. The PeNN\'s capture extrapolation and interpolation very well, contrary to the NN\'s. In addition, we have found that the NN\'s hyperparameters including network complexity and optimization methods do not have any effect on the above conclusions. We suggest that encoding NN\'s with any disciplinary system based information yields promise to better predict properties of complex systems than NN\'s alone, which will be in particular advantageous for small numbers of data. Such encoding would also be scalable, allowing different properties to be combined, without repetitive training of the NN\'s.
摘要：
预测复杂多尺度系统的物理特性是一个共同的挑战，需要对各种时空尺度进行分析。然而,由于缺乏对系统某些细节的了解，单靠物理学往往是不够的。有足够的数据，然而,机器学习技术可能会有所帮助。如果数据获取起来相对繁琐，混合方法可能会拯救。我们在本报告中着重于使用各种类型的神经网络（NN），包括将物理信息编码到其中的NN（PeNN），并研究了NN超参数的影响。我们应用网络来预测乳液的粘度作为剪切速率的函数。我们证明，使用各种网络性能指标作为均方误差和确定系数(R2)，PeNN总是比NN表现得更好，p值小于0.0002的弗里德曼检验也证实了这一点。PeNN的捕获外推和插值非常好，与NN相反。此外,我们发现神经网络的超参数包括网络复杂度和优化方法对上述结论没有任何影响。我们建议使用任何基于学科系统的信息对NN进行编码可以比单独使用NN更好地预测复杂系统的属性，这将特别有利于少量的数据。这样的编码也是可伸缩的，允许不同的属性组合，没有对NN进行重复训练。
