Identification

Title

Karhunen-LoÃ¨ve deep learning method for surrogate modeling and approximate Bayesian parameter estimation

Abstract

We evaluate the performance of the Karhunenâ€“LoÃ¨ve Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunenâ€“LoÃ¨ve (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-aposteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-theart Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

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document

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Unique resource identifier

code

https://n2t.net/ark:/85065/d7fn1bnr

codeSpace

Dataset language

eng

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geoscientificInformation

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Text

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title

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reference date

date type

publication

effective date

2016-01-01T00:00:00Z

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publication

effective date

2025-09-01T00:00:00Z

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Copyright author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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None

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contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

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pointOfContact

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