This paper studies the problem of dynamical system modeling, which involves the evolution of multiple interacting objects. Recent data-driven methods often utilize graph neural networks (GNNs) to learn these interactions by optimizing the neural network in an end-to-end fashion. While large language models (LLMs) have shown exceptional zero-shot performance across various applications, their potential for modeling dynamical systems has not been extensively explored. In this work, we design prompting techniques for dynamical system modeling and systematically evaluate the capabilities of LLMs on two tasks, including dynamic forecasting and relational reasoning. An extensive benchmark LLM4DS across nine datasets is built for performance comparison. Our extensive experiments yield several key findings: (1) LLMs demonstrate competitive performance without training compared to state-of-the-art methods in dynamical system modeling. (2) LLMs effectively infer complex interactions among objects to capture system evolution. (3) Prompt engineering plays a crucial role in enabling LLMs to accurately understand and predict the evolution of systems.

Supervised fine-tuning (SFT) is crucial in adapting large language models (LLMs) to a specific domain or task. However, only a limited amount of labeled data is available in practical applications, which poses a severe challenge for SFT in yielding satisfactory results. Therefore, a data-efficient framework that can fully exploit labeled and unlabeled data for LLM fine-tuning is highly anticipated.Towards this end, we introduce a **semi-supervised fine-tuning (SemiFT)** task and a framework named **SemiEvol** for LLM alignment from a propagate-and-select manner. For knowledge propagation, SemiEvol adopts a bi-level approach, propagating knowledge from labeled data to unlabeled data through both in-weight and in-context methods. For knowledge selection, SemiEvol incorporates a collaborative learning mechanism, selecting higher-quality pseudo-response samples. We conducted experiments using GPT-4o-mini and Llama-3.1 on seven general or domain-specific datasets, demonstrating significant improvements in model performance on target data. Furthermore, we compared SemiEvol with SFT and self-evolution methods, highlighting its practicality in hybrid data scenarios. Github Repository: [https://github.com/luo-junyu/SemiEvol](https://github.com/luo-junyu/SemiEvol).