用多模态大模型修正随机微分方程求解误差，兼顾速度与精度。
FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction
- 基于提示学习的解码器架构，融合数值与文本信息进行通用误差校正。
- 在分子动力学、金融等多领域测试中，精度效率优于传统求解器。
- 无需针对每类问题重新训练，适合跨领域快速模拟需求。
快速准确地模拟动态系统是科学与工程领域的基础挑战。传统数值积分器常在精度与计算效率间权衡，而现有神经网络方法通常需为每个场景单独训练模型。为此，我们提出一种用于大规模微分方程模拟的多模态基础模型：FMint-SDE（基于初始化的随机微分方程基础模型）。该模型采用仅解码器结构的Transformer，结合上下文学习能力，通过数值解与文本信息联合学习通用误差修正机制。训练时使用经典求解器生成的粗略解序列作为输入，实现对多种系统任务的广泛泛化。我们在涵盖分子动力学、机械系统、金融及生物学等多个领域的挑战性随机微分方程基准上进行了评估。实验表明，本方法在精度-效率权衡上显著优于经典求解器，展现出作为通用动态系统仿真工具的巨大潜力。
原文摘要 · Abstract (English)
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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