Deep Learning of Dynamical System Parameters from Return Maps as Images
Connor James Stephens Emmanuel Blazquez
We present a novel approach to system identification (SI) using deep learning
techniques. Focusing on parametric system identification (PSI), we use a
supervised learning approach for estimating the parameters of discrete and
continuous-time dynamical systems, irrespective of chaos. To accomplish this,
we transform collections of state-space trajectory observations into image-like
data to retain the state-space topology of trajectories from dynamical systems
and train convolutional neural networks to estimate the parameters of dynamical
systems from these images. We demonstrate that our approach can learn parameter
estimation functions for various dynamical systems, and by using training-time
data augmentation, we are able to learn estimation functions whose parameter
estimates are robust to changes in the sample fidelity of their inputs. Once
trained, these estimation models return parameter estimations for new systems
with negligible time and computation costs.