pyPCGA

Python library for Principal Component Geostatistical Approach

version 0.1

updates

• Exact preconditioner construction (inverse of cokriging/saddle-point matrix) using generalized eigendecomposition [Lee et al., WRR 2016, Saibaba et al, NLAA 2016]
• Fast hyperparameter tuning and predictive model validation using cR/Q2 criteria [Kitanidis, Math Geol 1991] ([Lee et al., 2021 in preparation])
• Fast posterior variance/std computation using exact preconditioner

version 0.2 will include

• automatic covariance model parameter calibration with nearshore application example
• link with FMM and HMatrix to support unstructured grids

Installation

python -m pip install git+https://github.com/jonghyunharrylee/pyPCGA.git

Courses

• UH CEE696 course on data assimilation

Example Notebooks

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!

Credits

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:

• Jonghyun Harry Lee
• Matthew Farthing
• Ty Hesser (STWAVE example)

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

References

• 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

Applications

• 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