Generating discrete dynamical system equations from input–output data using neural network identification models

This research presents a novel framework for generating equations describing discrete dynamical systems from only input–output data. The framework operates in two steps, creating a system identification model from input–output data using neural networks and then performing sensitivity analysis on the model. The sensitivity analysis is driven by a uniquely constrained functional decomposition of the identification model that breaks a complex identification problem into a group of small curve fitting problems. The resultant system equation represents the neural network identification model and by proxy the original system from which the input–output data belongs. The analysis allows for system equations to be generated from both black box systems and identification models, which can then be used for transparent and interpretable replacement of opaque system models. Transparent models can be better understood, leading to increased trustworthiness, safety, and reliability. An open source code implementation of the framework is created and made publicly available.