Xiaole Zhang

Shixuan Li, Wei Yang, Peiyu Zhang et al.

Weather forecasting is crucial for public safety, disaster prevention and mitigation, agricultural production, and energy management, with global relevance. Although deep learning has significantly advanced weather prediction, current methods face critical limitations: (i) they often struggle to capture both dynamic temporal dependencies and short-term abrupt changes, making extreme weather modeling difficult; (ii) they incur high computational costs due to extensive training and resource requirements; (iii) they have limited adaptability to multi-scale frequencies, leading to challenges when separating global trends from local fluctuations. To address these issues, we propose ClimateLLM, a foundation model for weather forecasting. It captures spatiotemporal dependencies via a cross-temporal and cross-spatial collaborative modeling framework that integrates Fourier-based frequency decomposition with Large Language Models (LLMs) to strengthen spatial and temporal modeling. Our framework uses a Mixture-of-Experts (MoE) mechanism that adaptively processes different frequency components, enabling efficient handling of both global signals and localized extreme events. In addition, we introduce a cross-temporal and cross-spatial dynamic prompting mechanism, allowing LLMs to incorporate meteorological patterns across multiple scales effectively. Extensive experiments on real-world datasets show that ClimateLLM outperforms state-of-the-art approaches in accuracy and efficiency, as a scalable solution for global weather forecasting.

Xiaole Zhang, Peiyu Zhang, Xiongye Xiao et al.

Integer-order calculus often falls short in capturing the long-range dependencies and memory effects found in many real-world processes. Fractional calculus addresses these gaps via fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control due to the lack of standard control methodologies. In this paper, we theoretically derive the optimal control via linear quadratic regulator (LQR) for fractional-order linear time-invariant (FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing an innovative system identification method control strategy for FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, Fractional-Order Learning for Optimal Control (FOLOC), that learns control policies from observed trajectories, and (iii) deriving a theoretical analysis of sample complexity to quantify the number of samples required for accurate optimal control in complex real-world problems. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control.