Human-designed algorithms have long been fundamental in solving a variety of scientific and engineering challenges. Recently, data-driven deep learning methods have also risen to prominence, offering innovative solutions across numerous scientific fields. While traditional algorithms excel in capturing the core aspects of specific problems, they often lack the flexibility needed for varying problem conditions due to the absence of specific data. Conversely, while data-driven approaches utilize vast datasets, they frequently fall short in domain-specific knowledge. To bridge these gaps, we introduce \textbf{FMint} (Foundation Model based on Initialization), a generative pre-trained model that synergizes the precision of human-designed algorithms with the adaptability of data-driven methods. This model is specifically engineered for high-accuracy simulation of dynamical systems. Starting from initial trajectories provided by conventional methods, FMint quickly delivers highly accurate solutions. It incorporates in-context learning and has been pre-trained on a diverse corpus of 500,000 dynamical systems, showcasing exceptional generalization across a broad spectrum of real-world applications. By effectively combining algorithmic rigor with data-driven flexibility, FMint sets the stage for the next generation of scientific foundation models, tackling complex problems with both efficiency and high accuracy.

翻译：长期以来，人工设计的算法一直是解决各类科学与工程挑战的基础。近年来，数据驱动的深度学习方法也崭露头角，为众多科学领域提供了创新方案。传统算法虽擅长捕捉特定问题的核心要素，但常因缺乏特定数据而难以适应多变的工况条件；而数据驱动方法虽能利用海量数据集，却往往欠缺领域专业知识。为弥合这一鸿沟，我们提出**FMint**（基于初始化的基础模型）——一种兼具人工设计算法精准性与数据驱动方法适应性的生成式预训练模型。该模型专为高精度动力学系统仿真而设计。FMint以传统方法提供的初始轨迹为起点，可快速输出高精度求解结果。它具备上下文学习能力，并在包含50万个动力学系统的多样化语料库上完成预训练，展现出对广泛实际应用场景的卓越泛化性能。FMint通过有效融合算法的严谨性与数据驱动的灵活性，为下一代科学基础模型奠定基础，能够以高效率和强精度应对复杂问题。