Catch-22s of reservoir computing

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.Comment: Published version (slight change to the title due to journal policy). Code at https://github.com/spcornelius/RCBasin

Do higher-order interactions promote synchronization?

Understanding how nonpairwise interactions alter dynamical processes in networks is of fundamental importance to the characterization and control of many coupled systems. Recent discoveries of hyperedge-enhanced synchronization under various settings raised speculations that such enhancements might be a general phenomenon. Here, we demonstrate that even for simple systems such as Kuramoto oscillators, the effects of higher-order interactions are highly representation-dependent. Specifically, we show numerically and analytically that hyperedges typically enhance synchronization in random hypergraphs, but have the opposite effect in simplicial complexes. As an explanation, we identify higher-order degree heterogeneity as the key structural determinant of synchronization stability in systems with a fixed coupling budget. Our findings highlight the importance of appropriate representations in describing higher-order interactions. In particular, the choice of simplicial complexes or hypergraphs has significant ramifications and should not be purely motivated by technical conveniences.Comment: Comments welcome! Y.Z. and M.L. contributed equally to this work. Code available at https://github.com/maximelucas/higherorder_sync_promote

Forest management policies and resource balance in China: an assessment of the current situation

Working paper du GATE 2007-12Using the latest forest inventory, this paper provides a comprehensive analysis of China's forest sector by focusing on new forest trends, forest policy changes and challenges to achieve a sustainable forest management. We analyze the dynamics of forest resources and provide an impact assessment of forest policies on China's forestry development over the last decades. Moreover, the analysis of the forest market highlights substantial disequilibria marked by a limited domestic supply potential and a growing demand for forest products satisfied by increasing imports. Internal and external solutions are explored and their implications for China and supplying countries are assessed