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Modeling and Control of Dynamical Systems with Reservoir Computing

Canaday, Daniel M
http://rave.ohiolink.edu/etdc/view?acc_num=osu157469471458874

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Physics.
There is currently great interest in applying artificial neural networks to a host of commercial and industrial tasks. Such networks with a layered, feedforward structure are currently deployed in technologies ranging from facial recognition software to self-driving cars. They are favored by a large portion of machine learning experts for a number of reasons. Namely: they possess a documented ability to generalize to unseen data and handle large data sets; there exists a number of well-understood training algorithms and integrated software packages for implementing them; and they have rigorously proven expressive power making them capable of approximating any bounded, static map arbitrarily well. Within the last couple of decades, reservoir computing has emerged as a method for training a different type of artificial neural network known as a recurrent neural network. Unlike layered, feedforward neural networks, recurrent neural networks are non-trivial dynamical systems that exhibit time-dependence and dynamical memory. In addition to being more biologically plausible, they more naturally handle time-dependent tasks such as predicting the load on an electrical grid or efficiently controlling a complicated industrial process. Fully-trained recurrent neural networks have high expressive power and are capable of emulating broad classes of dynamical systems. However, despite many recent insights, reservoir computing remains relatively young as a field. It remains unclear what fundamental properties yield a well-performing reservoir computer. In practice, this results in their design being left to domain experts, despite the actual training process being remarkably simple to implement. In this thesis, I describe a number of numerical and experimental results that expand the understanding and application of reservoir computing techniques. I develop an algorithm for controlling unknown dynamical systems with layers of reservoir computers. I demonstrate this algorithm by stabilizing a range of complex behavior in simulated Lorenz and Mackey-Glass systems. I additionally control an experimental, chaotic circuit with fast fluctuations. Using my technique, I demonstrate control within the measured noise level for some trajectories. This control algorithm is executed on a lightweight, readily-available platform with a 1 MHz closed-loop controller. I also develop a reservoir computing scheme with autonomous, Boolean networks capable of processing complex, real-valued data. I show that this system is capable of emulating, in real time, a benchmark chaotic time-series with high precision and a record-breaking speed of 160 million predictions per second. Finally, I present a technique for obtaining efficient, low dimensional reservoir computers. I demonstrate with numerical examples that the efficient reservoir computers can predict a benchmark time-series more accurately than standard reservoir computers 25 times larger. Through a linear analysis, I find that these efficient reservoirs prefer specific topologies over the random, unstructured reservoir computers that are currently standard.
Daniel Gauthier (Advisor)
Gregory Lafyatis (Committee Member)
Dick Furnstahl (Committee Member)
Mikhail Belkin (Committee Member)
Christopher Zirkle (Committee Member)
169 p.
Physics
dynamical systems; reservoir computing; recurrent neural networks; artificial neural networks; control engineering; time-series prediction

Recommended Citations

Citations

  • Canaday, D. M. (2019). Modeling and Control of Dynamical Systems with Reservoir Computing [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu157469471458874

    APA Style (7th edition)

  • Canaday, Daniel. Modeling and Control of Dynamical Systems with Reservoir Computing. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu157469471458874.

    MLA Style (8th edition)

  • Canaday, Daniel. "Modeling and Control of Dynamical Systems with Reservoir Computing." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu157469471458874

    Chicago Manual of Style (17th edition)

osu157469471458874
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This open access ETD is published by The Ohio State University and OhioLINK.