Data driven Dirichlet sampling on manifolds
This method offers a potentially more efficient way to sample data on manifolds, which could benefit neural network training, uncertainty analysis, and stochastic optimization for researchers and practitioners in these fields.
This paper introduces a new method for sampling on manifolds using the Dirichlet distribution, which allows for efficient and massive sampling while respecting the manifold's underlying structure. The method was tested on three different manifolds and applied to an engineering problem involving gas seal coefficients.
This article presents a novel method to sampling on manifolds based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data is observed, and to do massive samplings 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 considered to test the proposed methodology, and then it is employed to an engineering application, related to gas seal coefficients.