Recurrent Neural Networks for Partially Observed Dynamical Systems
This work addresses the challenge of handling unobserved state variables in nonlinear dynamics, offering a method that enhances interpretability for researchers in fields like physics and engineering, though it appears incremental as it builds on existing delay embedding and RNN techniques.
The paper tackles the problem of modeling partially observed dynamical systems by providing an algebraic approach to delay embedding that allows explicit error approximation and can be implemented using Recurrent Neural Networks (RNNs). This expands interpretability and facilitates structured incorporation into these methods.
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables. Here we provide an algebraic approach to delay embedding that permits explicit approximation of error. We also provide the asymptotic dependence of the first order approximation error on the system size. More importantly, this formulation of delay embedding can be directly implemented using a Recurrent Neural Network (RNN). This observation expands the interpretability of both delay embedding and RNN and facilitates principled incorporation of structure and other constraints into these approaches.