Sean P. Cornelius

Yuanzhao Zhang, Sean P. Cornelius

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty in the exact nonlinearity can render prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.

Yuanzhao Zhang, Edmilson Roque dos Santos, Huixin Zhang et al.

It has been found recently that more data can, counter-intuitively, hurt the performance of deep neural networks. Here, we show that a more extreme version of the phenomenon occurs in data-driven models of dynamical systems. To elucidate the underlying mechanism, we focus on next-generation reservoir computing (NGRC) -- a popular framework for learning dynamics from data. We find that, despite learning a better representation of the flow map with more training data, NGRC can adopt an ill-conditioned ``integrator'' and lose stability. We link this data-induced instability to the auxiliary dimensions created by the delayed states in NGRC. Based on these findings, we propose simple strategies to mitigate the instability, either by increasing regularization strength in tandem with data size, or by carefully introducing noise during training. Our results highlight the importance of proper regularization in data-driven modeling of dynamical systems.

Michael M. Danziger, Omkar R. Gojala, Sean P. Cornelius

Though robustness of networks to random attacks has been widely studied, intentional destruction by an intelligent agent is not tractable with previous methods. Here we devise a single-player game on a lattice that mimics the logic of an attacker attempting to destroy a network. The objective of the game is to disable all nodes in the fewest number of steps. We develop a reinforcement learning approach using deep Q-learning that is capable of learning to play this game successfully, and in so doing, to optimally attack a network. Because the learning algorithm is universal, we train agents on different definitions of robustness and compare the learned strategies. We find that superficially similar definitions of robustness induce different strategies in the trained agent, implying that optimally attacking or defending a network is sensitive the particular objective. Our method provides a new approach to understand network robustness, with potential applications to other discrete processes in disordered systems.