This article presents a new method to sample on manifolds, based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data are observed, and to do massive sampling with low computational effort. This can be very helpful, for instance, in neural networks training process, as well as in uncertainty analysis and stochastic optimization. Due to its simplicity and efficiency, we believe that the new method has great potential. Three manifolds (two dimensional ring, Mobius strip and spider geometry) are used to test the proposed methodology, and then it is employed to an engineering application, related to the bearing coefficients of a rotating machine. In the application, data are augmented to train a neural network.

本文提出了一种基于 Dirichlet 分布的流形采样新方法。所提出的策略允许完全尊重观察数据的潜在流形，并以低计算工作量进行大规模采样。这可能非常有用，例如，在神经网络训练过程中，以及在不确定性分析和随机优化中。由于其简单和高效，我们相信新方法具有巨大的潜力。三个流形（二维环、莫比乌斯带和蜘蛛几何）用于测试所提出的方法，然后将其用于与旋转机器轴承系数相关的工程应用。在应用程序中，数据被扩充以训练神经网络。