A Novel Approach to System Identification using Artificial Neural Networks

使用人工神经网络进行系统识别的新方法

• 批准号: 2016004
• 负责人: Jeffrey Moehlis
• 金额: $ 38.34万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2016004&HistoricalAwards=false
• 关键词: Novel; Approach; System; Identification; using

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.

精确的数学模型对于物理、生物和技术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，其中重要的潜在过程非常复杂或不太清楚，但可以获得充足的数据。在这种情况下，系统识别是一个强大的工具，可用于从观测数据推断数学模型。该研究将使用人工神经网络，一种强大的机器学习形式，在具有必要复杂性和非线性的模型中动态生成术语，以准确描述系统的动态。这种系统识别的新方法也将对非生物系统有用，包括几乎任何“黑箱”建模方法的系统，这种方法在没有任何详细了解模型内部工作原理的情况下进行预测。该研究将通过多层、基于运算的符号回归方法来完成常微分方程模型的系统识别，并通过训练适当的人工神经网络来学习复合运算。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字典，这限制了可以获得的可能模型。这种新方法为符号回归提供了一种强大的替代遗传规划策略，并且可以利用人工神经网络的许多吸引人的特征，例如直接的学习策略和大量关于扩展和优化的研究。该策略将适用于符号降维、对称性和约束的处理、噪声系统随机微分方程模型的识别、模型隐变量的确定以及候选Lyapunov函数的生成，该函数可用于证明给定模型的平衡解的稳定性。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。