Python library for Principal Component Geostatistical Approach
version 0.1
updates
version 0.2 will include
python -m pip install git+https://github.com/jonghyunharrylee/pyPCGA.git
1D linear inversion example below will be helpful to understand how pyPCGA can be implemented. Please check Google Colab examples.
1D linear inversion example (from Stanford 362G course) Google Colab example
1D nonlinear inversion example (from Stanford 362G course) Google Colab example
Hydraulic conductivity estimation example using USGS-FloPy (MODFLOW) [Lee and Kitanidis, 2014] Google Colab example
Tracer tomography example using Crunch (with Mahta Ansari from UIUC Druhan Lab)
Bathymetry estimation example using STWAVE (with USACE-ERDC-CHL)
Permeability estimation example using TOUGH2 (with Amalia Kokkianki, USFCA)
Electrical conductivity estimation example using magnetotelluric (MT) survey with MARE2DEM (with Niels Grobbe, UHM)
DNAPL plume estimation using hydraulic head, self-potential (SP) and partitioning tracer data (with Xueyuan Kang et al.)
ERT example using E4D will be completed soon.
MODFLOW-USG/SEAWAT/MODFLOW6 examples coming soon!
pyPCGA is based on Lee et al. [2016] and currently used for Stanford-USACE ERDC project led by EF Darve and PK Kitanidis and NSF EPSCoR `Ike Wai project.
Code contributors include:
FFT-based matvec code is adapted from Arvind Saibaba's work (https://github.com/arvindks/kle).
FMM-based code (https://arxiv.org/abs/1903.02153) will be incorporated in version 0.2
J Lee, H Yoon, PK Kitanidis, CJ Werth, AJ Valocchi, "Scalable subsurface inverse modeling of huge data sets with an application to tracer concentration breakthrough data from magnetic resonance imaging", Water Resources Research 52 (7), 5213-5231
AK Saibaba, J Lee, PK Kitanidis, Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen–Loève expansion, Numerical Linear Algebra with Applications 23 (2), 314-339
J Lee, PK Kitanidis, "Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)", WRR 50 (7), 5410-5427
PK Kitanidis, J Lee, Principal Component Geostatistical Approach for large‐dimensional inverse problems, WRR 50 (7), 5428-5443
T. Kadeethum, D. O'Malley, JN Fuhg, Y. Choi, J. Lee, HS Viswanathan and N. Bouklas, A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks, Nature Computational Science, 819–829, 2021
J Lee, H Ghorbanidehno, M Farthing, T. Hesser, EF Darve, and PK Kitanidis, Riverine bathymetry imaging with indirect observations, Water Resources Research, 54(5): 3704-3727, 2018
J Lee, A Kokkinaki, PK Kitanidis, Fast large-scale joint inversion for deep aquifer characterization using pressure and heat tracer measurements, Transport in Porous Media, 123(3): 533-543, 2018
PK Kang, J Lee, X Fu, S Lee, PK Kitanidis, J Ruben, Improved Characterization of Heterogeneous Permeability in Saline Aquifers from Transient Pressure Data during Freshwater Injection, Water Resources Research, 53(5): 4444-458, 2017
S. Fakhreddine, J Lee, PK Kitanidis, S Fendorf, M Rolle, Imaging Geochemical Heterogeneities Using Inverse Reactive Transport Modeling: an Example Relevant for Characterizing Arsenic Mobilization and Distribution, Advances in Water Resources, 88: 186-197, 2016