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.

翻译：我们提出了一种利用深度学习技术进行系统辨识（SI）的新方法。该方法聚焦于参数系统辨识（PSI），采用监督学习途径估计离散和连续时间动力学系统（无论混沌与否）的参数。为实现这一目标，我们将状态空间轨迹观测集合转化为类似图像的数据，以保留动力学系统轨迹的状态空间拓扑结构，并训练卷积神经网络从这些图像中估计动力学系统参数。我们证明该方法能够为多种动力学系统学习参数估计函数，且通过训练时数据增强，可习得对输入样本保真度变化具有鲁棒性的参数估计函数。一旦训练完成，这些估计模型能以可忽略的时间和计算成本为新系统返回参数估计结果。