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Debriefing Neural Networks for Nonlinear Dynamics

This is a new collaborative project between Princeton University and the Technical University of Munich.

In the early 1990s, before the modern advent of easy general-purpose GPU computing and the attendant boom in deep learning as the dominant paradigm in machine learning, smaller artifical neural networks (ANNs) still enjoyed some use in process control.

Various methods have been employed to use ANNs to represent the dynamical system underlying corpi of timeseries data, coupled with several dimensionality reduction techniques for ensuring smooth and robust behavior of the resulting models. These system identification techniques have the advantage of being readily parameterized, allowing for rigorous bifurcation analysis, and are cheap to evaluate, allowing for use in real-time control. Being data-driven, they are also easy to apply, with little modification, to several different systems of interest.

This project aims to revive such techniques using modern deep learning frameworks such as Keras, Theano, and Tenserflow.

More importantly, we aim to transfer manifold learning techniques developed in other projects for application in several places in this endeavor. In addition to using these techniques as an alternative to the dimensionality reduction methods used as part of this existing system-identification strategy, our manifold learning techniques can be used for the simplification of generated networks, and as an analysis technique for ganing insight into how the network learns specific dynamic features.

This final point could lead to future applications to biological neural networks, accelerating work on the seemingly contradictory fundamental task of neuroscience--understanding our own understanding.