Probabilistic models and sampling on manifolds

Abstract : We present a new approach for sampling probability models supported on a manifold. The manifold is characterized through its manifold diffusion subspace, the probability model is constructed using kernel density estimation and sampling is carried out using a Ito equation projected on the manifold. The procedure serves a number of objectives that are ubiquitous in uncertainty quantification. First, by acknowledging an intrinsic structure discovered from numerically generated simulations, their scatter associated with parametric variations is considerably smaller than viewed in an ambient space. Fewer may thus be required to achieve similar statistical precision. This capability is even more significant for OUU problems where the stochastic simulator is integrated into an optimization loop. We demonstrate this capability on high-dimensional UQ problems with very expensive forward simulators. Second, the projected Ito provides an accurate probabilistic surrogate for large high-dimensional datasets.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01810459
Contributor : Christian Soize <>
Submitted on : Thursday, June 7, 2018 - 10:21:01 PM
Last modification on : Friday, October 4, 2019 - 1:31:54 AM

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  • HAL Id : hal-01810459, version 1

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Roger Ghanem, Christian Soize. Probabilistic models and sampling on manifolds. SIAM UQ, Apr 2018, Garden Grove, United States. ⟨hal-01810459⟩

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