A Novel Approach to System Identification using Artificial Neural Networks

精确的数学模型对物理、生物和技术系统的重要性怎么强调都不过分。 这些模型使研究人员能够理解，分析和预测这些系统的行为。 不幸的是，通常不可能从第一原理推导出数学模型，特别是对于许多生物系统，对于这些生物系统，重要的基本过程非常复杂或没有得到很好的理解，但是对于这些生物系统，可以获得足够的数据。 在这种情况下，系统辨识是一个强大的工具，可以用来推导数学模型从观察到的数据。 该研究将使用人工神经网络（一种强大的机器学习形式）来动态生成具有必要复杂性和非线性的模型中的项，以准确描述系统的动态。 这种新的系统辨识方法也将适用于非生物系统，包括几乎任何应用了“黑箱”建模方法的系统，这种方法在不详细了解模型内部工作原理的情况下进行预测。该研究将通过基于操作的多层符号回归方法来完成常微分方程模型的系统辨识，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的术语的字典，这限制了可以获得的可能的模型。 这种新的方法提供了一个强大的替代遗传编程策略的符号回归，并可以利用人工神经网络的许多有吸引力的功能，如一个简单的学习策略和一个大型语料库的研究扩展和优化。 该策略将被调整以允许符号维数减少、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、模型的隐变量的确定、以及产生候选李雅普诺夫函数，用于证明给定模型的平衡解的稳定性。该奖项反映了NSF的法定使命，并被认为是值得的通过使用基金会的知识价值和更广泛的影响审查标准进行评估来提供支持。

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.