Smita Deb

Smita Deb, Zheng-Meng Zhai, Mulugeta Haile et al.

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of parameter-adaptable reservoir computing has been applied to predict tipping in systems described by low-dimensional stochastic differential equations. However, anticipating tipping in complex spatiotemporal dynamical systems remains a significant open problem. The ability to forecast not only the occurrence but also the precise timing of such tipping events is crucial for providing the actionable lead time necessary for timely mitigation. By utilizing the mathematical approach of non-negative matrix factorization to generate dimensionally reduced spatiotemporal data as input, we exploit parameter-adaptable reservoir computing to accurately anticipate tipping. We demonstrate that the tipping time can be identified within a narrow prediction window across a variety of spatiotemporal dynamical systems, as well as in CMIP5 (Coupled Model Intercomparison Project 5) climate projections. Furthermore, we show that this reservoir-computing framework, utilizing reduced input data, is robust against common forecasting challenges and significantly alleviates the computational overhead associated with processing full spatiotemporal data.

Smita Deb, Shirin Panahi, Mulugeta Haile et al.

Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems remains a significant challenge. This paper proposes a physical RC scheme inspired by the biological vestibular system. To overcome hardware complexity, we introduce a designed uncoupled topology and demonstrate that it achieves performance comparable to fully coupled networks. We theoretically analyze the difference between these topologies by deriving a memory capacity formula for linear reservoirs, identifying specific conditions where both configurations yield equivalent memory. These analytical results are demonstrated to approximately hold for nonlinear reservoir systems. Furthermore, we systematically examine the impact of reservoir size on predictive statistics and memory capacity. Our findings suggest that uncoupled reservoir architectures offer a mathematically sound and practically feasible pathway for efficient physical reservoir computing.