论文标题
参数$ p $ -dirichlet问题的深度丽思方法
The Deep Ritz Method for Parametric $p$-Dirichlet Problems
论文作者
论文摘要
我们建立了用于部署深里兹方法的参数$ p $ -dirichlet问题的近似值的错误估计。参数依赖项包括，例如，（1，\ infty）$变化的几何和指数$ p \。将导出的误差估计与定量近似定理相结合会产生误差衰减率，并确定深里兹方法在高维函数的近似值中保留了神经网络的有利近似能力，这使该方法使该方法对参数问题有吸引力。最后，我们提出数值示例，以说明潜在的应用。
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents $p\in (1,\infty)$. Combining the derived error estimates with quantitative approximation theorems yields error decay rates and establishes that the Deep Ritz Method retains the favorable approximation capabilities of neural networks in the approximation of high dimensional functions which makes the method attractive for parametric problems. Finally, we present numerical examples to illustrate potential applications.
