English(EN) Multifidelity Gaussian process regression for solving nonlinear partial differential equations

新的核学习方法利用多保真度数据解决非线性偏微分方程

作者 PulseAugur 编辑部 · [1 个来源] · 2026-05-11 11:24

研究人员开发了一种新的核学习方法，使用协同克里金法来求解非线性偏微分方程（PDE）。该方法利用来自多保真度模拟的经验信息，将可微分的非平稳核拟合到低保真度数据上。然后，该方法推导出高保真度核和均值，并将其集成到高斯过程框架中以求解PDE，在Burgers方程上证明了其有效性。 AI

影响引入了一种解决复杂微分方程的新方法，有可能提高科学模拟的准确性和速度。

排序理由该集群包含一篇详细介绍求解微分方程新方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv stat.ML TIER_1 English(EN) · Olivier Roustant · 2026-05-11 11:24

多保真高斯过程回归用于求解非线性偏微分方程

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work, as the available information is inheren…