A Novel Approach to System Identification using Artificial Neural Networks

精确的数学模型对于具有物理、生物和技术价值的系统的重要性怎么强调都不为过。这些模型使研究人员能够了解、分析和预测此类系统的行为。不幸的是，从第一原理推导出数学模型往往是不可能的，特别是对于许多生物系统来说，对于这些系统，重要的潜在过程极其复杂或没有得到很好的理解，但可以获得大量的数据。在这种情况下，系统辨识是一个强大的工具，可以用来从观测数据中推导出数学模型。这项研究将使用人工神经网络，这是一种强大的机器学习形式，以动态地生成模型中的项，并具有必要的复杂性和非线性，以准确描述系统的动态。这种新的系统辨识方法对非生物系统也是有用的，包括几乎任何应用了黑箱建模方法的系统，这种建模方法在不详细了解模型内部工作原理的情况下对其进行预测。研究将通过一种基于运算的多层符号回归方法来完成常微分方程式模型的系统辨识，并具有通过训练适当的人工神经网络来学习复合运算的能力。与许多现有的系统识别技术不同，它不需要预先指定可能术语的词典，这限制了可以获得的可能模型。这种新的方法为符号回归的遗传编程策略提供了一种强大的替代方案，并可以利用人工神经网络的许多吸引人的特征，例如简单的学习策略和大量关于扩展和优化的研究语料库。这一策略将被调整以允许符号降维，对称性和约束的处理，噪声系统的随机微分方程模型的识别，模型的隐藏变量的确定，以及可用于证明给定模型的平衡解的稳定性的候选Lyapunov函数的生成。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The importance of accurate mathematical models for systems of physical, biological, and technological interest cannot be overstated. These models allow researchers to understand, analyze, and predict the behavior of such systems. Unfortunately, it is often impossible to derive mathematical models from first principles, in particular for many biological systems, for which important underlying processes are exceedingly complex or are not well understood, but for which ample data can be obtained. In such cases, system identification is a powerful tool which can be used to deduce mathematical models from observed data. The research will use artificial neural networks, a powerful form of machine learning, to dynamically generate the terms in a model with the necessary complexity and nonlinearity to accurately describe a system's dynamics. This new method of system identification will be also useful for non-biological systems, including virtually any system for which "black box" modeling approaches, which make predictions without any detailed understanding of the inner workings of the model, have been applied.The research will accomplish system identification of ordinary differential equation models through a multilayered, operation-based symbolic regression approach, with the capacity to learn compound operations by training appropriate artificial neural networks. Unlike many existing system identification techniques, it does not require pre-specification of a dictionary of possible terms, which constrain the possible models which can be obtained. This new approach provides a powerful alternative to genetic programming strategies for symbolic regression, and can exploit many of the attractive features of artificial neural networks such as a straightforward learning strategy and a large corpus of research on extensions and optimizations. This strategy will be adapted to allow for symbolic dimension reduction, the treatment of symmetries and constraints, the identification of stochastic differential equation models for noisy systems, the determination of hidden variables for the models, and the generation of candidate Lyapunov functions which can be used to prove the stability of equilibrium solutions to given models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.