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Title: Distance-preserving manifold denoising for data-driven mechanics
This article introduces an isometric manifold embedding data-driven paradigm designed to enable model-free simulations with noisy data sampled from a constitutive manifold. The proposed data-driven approach iterates between a global optimization problem that seeks admissible solutions for the balance principle and a local optimization problem that finds the closest point projection of the Euclidean space that isometrically embeds a nonlinear constitutive manifold. To de-noise the database, a geometric autoencoder is introduced such that the encoder first learns to create an approximated embedding that maps the underlying low-dimensional structure of the high-dimensional constitutive manifold onto a flattened manifold with less curvature. We then obtain the noise-free constitutive responses by projecting data onto a denoised latent space that is completely flat by assuming that the noise and the underlying constitutive signal are orthogonal to each other. Consequently, a projection from the conservative manifold onto this de-noised constitutive latent space enables us to complete the local optimization step of the data-driven paradigm. Finally, to decode the data expressed in the latent space without reintroducing noise, we impose a set of isometry constraints while training the autoencoder such that the nonlinear mapping from the latent space to the reconstructed constituent manifold is distance-preserving. Numerical examples are used to both validate the implementation and demonstrate the accuracy, robustness, and limitations of the proposed paradigm.  more » « less
Award ID(s):
1846875
NSF-PAR ID:
10487110
Author(s) / Creator(s):
;
Publisher / Repository:
ScienceDirect
Date Published:
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Volume:
405
Issue:
C
ISSN:
0045-7825
Page Range / eLocation ID:
115857
Subject(s) / Keyword(s):
Data-driven mechanics Manifold de-noising Geodesic Constitutive manifold Autoencoder Isometry
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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