15,761 research outputs found
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential
to transform data-rich fields that lack well-characterized quantitative
descriptions. Advances in sparse regression are currently enabling the
tractable identification of both the structure and parameters of a nonlinear
dynamical system from data. The resulting models have the fewest terms
necessary to describe the dynamics, balancing model complexity with descriptive
ability, and thus promoting interpretability and generalizability. This
provides an algorithmic approach to Occam's razor for model discovery. However,
this approach fundamentally relies on an effective coordinate system in which
the dynamics have a simple representation. In this work, we design a custom
autoencoder to discover a coordinate transformation into a reduced space where
the dynamics may be sparsely represented. Thus, we simultaneously learn the
governing equations and the associated coordinate system. We demonstrate this
approach on several example high-dimensional dynamical systems with
low-dimensional behavior. The resulting modeling framework combines the
strengths of deep neural networks for flexible representation and sparse
identification of nonlinear dynamics (SINDy) for parsimonious models. It is the
first method of its kind to place the discovery of coordinates and models on an
equal footing.Comment: 25 pages, 6 figures; added acknowledgment
Feedback control by online learning an inverse model
A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made
Neural Networks for Modeling and Control of Particle Accelerators
We describe some of the challenges of particle accelerator control, highlight
recent advances in neural network techniques, discuss some promising avenues
for incorporating neural networks into particle accelerator control systems,
and describe a neural network-based control system that is being developed for
resonance control of an RF electron gun at the Fermilab Accelerator Science and
Technology (FAST) facility, including initial experimental results from a
benchmark controller.Comment: 21 p
Dynamical System Parameter Identification using Deep Recurrent Cell Networks
In this paper, we investigate the parameter identification problem in
dynamical systems through a deep learning approach. Focusing mainly on
second-order, linear time-invariant dynamical systems, the topic of damping
factor identification is studied. By utilizing a six-layer deep neural network
with different recurrent cells, namely GRUs, LSTMs or BiLSTMs; and by feeding
input-output sequence pairs captured from a dynamical system simulator, we
search for an effective deep recurrent architecture in order to resolve damping
factor identification problem. Our study results show that, although previously
not utilized for this task in the literature, bidirectional gated recurrent
cells (BiLSTMs) provide better parameter identification results when compared
to unidirectional gated recurrent memory cells such as GRUs and LSTM. Thus,
indicating that an input-output sequence pair of finite length, collected from
a dynamical system and when observed anachronistically, may carry information
in both time directions for prediction of a dynamical systems parameter.Comment: Final version published in Journal of Neural Computing and
Application
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