FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction

• URL: http://arxiv.org/abs/2510.27173v1
• Date: Fri, 31 Oct 2025 04:49:41 GMT
• Title: FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction
• Authors: Jiaxin Yuan, Haizhao Yang, Maria Cameron,
• Abstract summary: We introduce a novel multi-modal foundation model for large-scale simulations of differential equations: FMint-SDE.<n>Based on a decoder-only transformer with in-context learning, FMint-SDE learns a universal error-correction scheme.<n>We evaluate our models on a suite of challenging SDE benchmarks spanning applications in molecular dynamics, mechanical systems, finance, and biology.
• Score: 7.463977095236658
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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