## Discovering Dynamical Parameters by Interpreting Echo State Networks

24 Sept 2021, 16:11 (modified: 01 Dec 2021, 20:09)NeurIPS-AI4Science OralReaders: Everyone
Keywords: nonlinear dynamics, echo state networks, reservoir computing, interpretability, manifold learning, unsupervised learning
TL;DR: We identify and extract parameters governing the dynamics of a chaotic nonlinear system by interpreting the learned readout layer of an echo state network as a representation of the system dynamics.
Abstract: Reservoir computing architectures known as echo state networks (ESNs) have been shown to have exceptional predictive capabilities when trained on chaotic systems. However, ESN models are often seen as black-box predictors that lack interpretability. We show that the parameters governing the dynamics of a complex nonlinear system can be encoded in the learned readout layer of an ESN. We can extract these dynamical parameters by examining the geometry of the readout layer weights through principal component analysis. We demonstrate this approach by extracting the values of three dynamical parameters ($\sigma$, $\rho$, $\beta$) from a dataset of Lorenz systems where all three parameters are varying among different trajectories. Our proposed method not only demonstrates the interpretability of the ESN readout layer but also provides a computationally inexpensive, unsupervised data-driven approach for identifying uncontrolled variables affecting real-world data from nonlinear dynamical systems.
Track: Original Research Track