edu.ucar.opensky::articles:43873 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-24T17:43:38.534861 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.net/ark:/85065/d7fn1bnr https://doi.org/10.5281/zenodo.15381308 https Related ComputationalNotebook #1 KL-DNN Freyberg Steady State https://doi.org/10.48550/arXiv.2312.06177 https Related Preprint #1 Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems Karhunen-Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation 2025-09-01T00:00:00Z publication https://n2t.net/ark:/85065/d7fn1bnr https://doi.org/10.1016/j.advwatres.2025.105024 Wang, Y. author Zong, Y. author McCreight, James author Joseph D. Hughes author Fienen, M. author Tartakovsky, A. M. author UCAR/NCAR - Library publisher <p>We evaluate the performance of the Karhunen–Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen–Loève (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.&nbsp;</p><p>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.</p> UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication <span style="font-family:Arial;font-size:10pt;font-style:normal;" data-sheets-root="1">Copyright author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.</span> None eng geoscientificInformation