Deep Learning of Dynamical System Parameters from Return Maps as Images

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.