论文标题
用于参数不确定性定量的随机深处 - 里兹
Stochastic Deep-Ritz for Parametric Uncertainty Quantification
论文作者
论文摘要
科学的机器学习已成为材料科学和工程学中越来越重要的工具。它特别适合解决涉及许多变量的材料问题，或者允许快速构建材料模型的替代物，仅举几例。从数学上讲，材料科学和工程中的许多问题都可以作为变异问题。然而，在材料中，在材料中存在的不确定性在变化配方中，对于科学机器学习而言仍然具有挑战性。在本文中，我们提出了一种基于深度学习的数值方法，用于解决不确定性下的变异问题。我们的方法无缝地将深度学习的近似与蒙特 - 卡洛采样相结合。所得的数值方法强大但非常简单。我们评估其在许多变化问题上的性能和准确性。
Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving many variables or to allow rapid construction of surrogates of material models, to name just a few. Mathematically, many problems in materials science and engineering can be cast as variational problems. However, handling of uncertainty, ever present in materials, in the context of variational formulations remains challenging for scientific machine learning. In this article, we propose a deep-learning-based numerical method for solving variational problems under uncertainty. Our approach seamlessly combines deep-learning approximation with Monte-Carlo sampling. The resulting numerical method is powerful yet remarkably simple. We assess its performance and accuracy on a number of variational problems.
