[论文] Multilevel Euler-Maruyama for Solving SDEs and ODEs with Deep Learning...

论文概要

研究领域: ML 作者: Arthur Jacot 发布时间: 2026-03-25 arXiv: 2603.24594

中文摘要

本文引入多级欧拉-丸山（ML-EM）方法，使用一系列精度递增、计算成本递增的漂移f近似器f^1,...,f^k来计算SDE和ODE的解，仅需少量评估最精确的f^k和大量评估成本较低的f^1,...,f^{k-1}。如果漂移处于所谓的难于蒙特卡洛（HTMC）状态，即需要epsilon^{-gamma}计算量才能达到epsilon近似（其中gamma大于2），则ML-EM可以用epsilon^{-gamma}计算量来epsilon近似SDE的解。

原文摘要

We introduce the Multilevel Euler-Maruyama (ML-EM) method compute solutions of SDEs and ODEs using a range of approximators f^1,...,f^k to the drift f with increasing accuracy and computational cost, only requiring a few evaluations of the most accurate f^k and many evaluations of the less costly f^1,...,f^{k-1}. If the drift lies in the so-called Harder than Monte Carlo (HTMC) regime, i.e. it requires epsilon^{-gamma} compute to be epsilon-approximated for some gamma>2, then ML-EM epsilon-approximates the solution of the SDE with epsilon^{-gamma} compute.

--- *自动采集于 2026-03-27*

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