FMint-SDE：一种多模态基础模型，通过误差校正加速微分方程的数值模拟
FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction
AI总结：
FMint-SDE通过多模态学习实现误差校正，提升微分方程数值模拟的精度与效率。
摘要：
快速且准确地模拟动态系统是科学和工程领域中的基本挑战。传统数值积分器往往在精度和计算效率之间面临权衡，而现有的基于神经网络的方法通常需要为每个案例单独训练一个模型。为克服这些限制，我们引入了一种新的多模态基础模型，用于大规模微分方程的模拟：FMint-SDE（基于初始化的随机微分方程基础模型）。该模型基于一个仅解码器的Transformer，并具有上下文学习能力，利用数值和文本模态来学习通用的误差校正方案。它通过由传统求解器生成的提示序列粗解来训练，使模型能够在各种系统中广泛泛化。我们在一系列具有挑战性的SDE基准测试中评估了我们的模型，涵盖分子动力学、机械系统、金融和生物学应用。实验结果表明，我们的方法在准确性和效率之间取得了优于传统求解器的权衡，凸显了FMint-SDE作为动态系统通用模拟工具的潜力。
英文摘要：
Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing neural network-based approaches typically require training a separate model for each case. To overcome these limitations, we introduce a novel multi-modal foundation model for large-scale simulations of differential equations: FMint-SDE (Foundation Model based on Initialization for stochastic differential equations). Based on a decoder-only transformer with in-context learning, FMint-SDE leverages numerical and textual modalities to learn a universal error-correction scheme. It is trained using prompted sequences of coarse solutions generated by conventional solvers, enabling broad generalization across diverse systems. We evaluate our models on a suite of challenging SDE benchmarks spanning applications in molecular dynamics, mechanical systems, finance, and biology. Experimental results show that our approach achieves a superior accuracy-efficiency tradeoff compared to classical solvers, underscoring the potential of FMint-SDE as a general-purpose simulation tool for dynamical systems.
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