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Deshpande S.♦, Rappel H.♦, Hobbs M.♦, Bordas S.♦, Lengiewicz J.A., Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids,
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2025.117790, Vol.437, No.117790, pp.1-17, 2025 Abstract:
Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input–output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments. Keywords:
Surrogate modeling,Deep neural networks,Gaussian proces,Autoencoders,Uncertainty quantification,Finite element method Affiliations:
| Deshpande S. | - | University of Luxembourg (LU) | | Rappel H. | - | other affiliation | | Hobbs M. | - | other affiliation | | Bordas S. | - | other affiliation | | Lengiewicz J.A. | - | IPPT PAN |
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