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Chaotic dynamics are ubiquitous in many real-world systems, ranging from biological and industrial processes to climate dynamics and the spread of viruses. These systems are characterized by high sensitivity to initial conditions, making it challenging to predict their future behavior confidently. In this study, we propose a novel deep-learning framework that addresses this challenge by directly exploiting the long-term compounding of local prediction errors during model training, aiming to extend the time horizon for reliable predictions of chaotic systems. Our approach observes the future trajectories of initial errors at a time horizon, modeling the evolution of the loss to that point through the use of two major components: 1) a recurrent architecture (Error Trajectory Tracing) designed to trace the trajectories of predictive errors through phase space, and 2) a training regime, Horizon Forcing, that pushes the model’s focus out to a predetermined time horizon. We validate our method on three classic chaotic systems and six real-world time series prediction tasks with chaotic characteristics. The results show that our approach outperforms the state-of-the-art methods. 

Front matter of the IEEE International Conference on Big Data (BigData 2024) proceedings, including General Chairs and organizing committee information. 

Abstract This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure. Then, a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response. The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams. The performance, evaluated both in terms of accuracy and computational efficiency, is directly contrasted with high-fidelity finite element models that fully resolve the pores’ geometry. Results indicate that the reduced-order representation of the porous microstructure, captured by the synthetic variable-order parameter, offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity. 

Metallic sulfide anodes show great promise for sodium‐ion batteries due to their high theoretic capacities. However, their practical application is greatly hampered by poor electrochemical performance because of the large volume expansion of the sulfides and the sluggish kinetics of the Na⁺ions. Herein, a porous bimetallic sulfide of the SnS/Sb₂S₃heterostructure is constructed that is encapsulated in the sulfur and nitrogen codoped carbon matrix (SnS/Sb₂S₃@SNC) by a facile and scalable method. The porous structure can provide void space to alleviate the volume expansion upon cycling, guaranteeing excellent structural stability. The unique heterostructure and the S, N codoped carbon matrix together facilitate fast‐charge transport to improve reaction kinetics. Benefitting from these merits, the SnS/Sb₂S₃@SNC electrode exhibits high capacities of 425 mA h g⁻¹at 200 mA g⁻¹after 100 cycles, and 302 mA h g⁻¹at 500 mA g⁻¹after 400 cycles. Moreover, the SnS/Sb₂S₃@SNC anode shows an outstanding rate performance with a capacity of over 200 mA h g⁻¹at a high current density of 5000 mA g⁻¹. This study provides a new strategy and insight into the design of electrode materials with the potential for the practical realization and applications of next‐generation batteries. 

The understanding of chaotic systems is challenging not only for theoretical research but also for many important applications. Chaotic behavior is found in many nonlinear dynamical systems, such as those found in climate dynamics, weather, the stock market, and the space-time dynamics of virus spread. A reliable solution for these systems must handle their complex space-time dynamics and sensitive dependence on initial conditions. We develop a deep learning framework to push the time horizon at which reliable predictions can be made further into the future by better evaluating the consequences of local errors when modeling nonlinear systems. Our approach observes the future trajectories of initial errors at a time horizon to model the evolution of the loss to that point with two major components: 1) a recurrent architecture, Error Trajectory Tracing, that is designed to trace the trajectories of predictive errors through phase space, and 2) a training regime, Horizon Forcing, that pushes the model’s focus out to a predetermined time horizon. We validate our method on classic chaotic systems and real-world time series prediction tasks with chaotic characteristics, and show that our approach outperforms the current state-of-the-art methods.