一种随机热方程的全离散非负保持有限元方法
机器学习
2026-02-19 v1
摘要
我们考虑一个随机热方程，其非线性有限秩空间彩色乘性噪声在给定非负初始数据时唯一存在非负解。灵感来自现有关于全离散有限差分方案的研究结果，并在半离散质量压总有限元近似的收敛分析基础上，引入一种全离散数值方法，将质量压总有限元与 Lie-Trotter 分割策略相结合。该离散化在离散层面保持非负性，并在适当的正则性条件下证明收敛。提供了严格的收敛分析，突出了质量压总在确保非负性方面的作用，以及分离策略在解耦确定性和随机动力学方面的作用。 presented numerical experiments are presented to confirm the convergence rates and the preservation of nonnegativity. Additionally, we examine several numerical examples beyond the scope of the established theory, aiming to explore the range of applicability and potential limitations of the proposed method.
引用
@article{arxiv.2602.16507,
title = {Small molecule retrieval from tandem mass spectrometry: what are we optimizing for?},
author = {Gaetan De Waele and Marek Wydmuch and Krzysztof Dembczyński and Wojciech Kotłowski and Willem Waegeman},
journal= {arXiv preprint arXiv:2602.16507},
year = {2026}
}