Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differential equation). Neural ODE has advantages like a possibly higher class of represented functions, the extended interpretability compared to black-box machine learning models, ability to describe both trend and local behaviour. Such advantages are especially critical for time series with complicated trends. However, the known drawback is the high training time compared to the autoregressive models and long-short term memory (LSTM) networks widely used for data-driven time series modelling. Therefore, we should be able to balance interpretability and training time to apply neural ODE in practice. The paper shows that modern neural ODE cannot be reduced to simpler models for time-series modelling applications. The complexity of neural ODE is compared to or exceeds the conventional time-series modelling tools. The only interpretation that could be extracted is the eigenspace of the operator, which is an ill-posed problem for a large system. Spectra could be extracted using different classical analysis methods that do not have the drawback of extended time. Consequently, we reduce the neural ODE to a simpler linear form and propose a new view on time-series modelling using combined neural networks and an ODE system approach.
翻译:多数机器学习方法被用作建模的黑盒。 我们可能会试图从基于物理的培训方法中提取一些知识,例如神经载体(普通差异方程式)等。神经载体具有一些优势,例如具有可能更高层次的代表性功能、与黑箱机学习模型相比可扩展的解释性、描述趋势和地方行为的能力。这些优势对于具有复杂趋势的时间序列来说尤为关键。然而,已知的缺点是,与自动反向模型和长期短期内存(LSTM)网络相比,培训时间过长。因此,我们应该能够平衡解释性和培训时间,以便在实践中应用神经载体代体。该文件表明,现代神经载体不能被压缩为更简单的时间序列建模应用模型模型模型。神经载的复杂程度与常规的时间序列建模工具相比或超过。唯一可以提取的解释是操作器的天体空间,这对大型系统来说是一个错误的问题。因此,我们可以用不同的古典分析方法来进行模拟,在实际中应用神经载体模型,因此,我们可以减少使用不简化的线内建模型,在新的时间序列上提出更简单的模型。