Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification. (arXiv:2401.16683v1 [stat.ML])

In this work we introduce a manifold learning-based surrogate modeling
framework for uncertainty quantification in high-dimensional stochastic
systems. Our first goal is to perform data mining on the available simulation
data to identify a set of low-dimensional (latent) descriptors that efficiently
parameterize the response of the high-dimensional computational model. To this
end, we employ Principal Geodesic Analysis on the Grassmann manifold of the
response to identify a set of disjoint principal geodesic submanifolds, of
possibly different dimension, that captures the …

arxiv chaos data data mining framework identify low manifold mining modeling polynomial quantification set simulation stat.ml stochastic systems uncertainty work