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.
