Related publications

A computationally efficient parallel <scp>L</scp>evenberg‐<scp>M</scp>arquardt algorithm for highly parameterized inverse model analyses (2016) — Youzuo Lin, Daniel O'Malley, Velimir V. Vesselinov — Water Resources Research
Abstract
Abstract Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg‐Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg‐Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large‐scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2‐D and a random hydraulic conductivity field in 3‐D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework ( http://mads.lanl.gov ). By comparing with Levenberg‐Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg‐Marquardt method yields a speed‐up ratio on the order of to in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large‐scale problems.
Robust Decision Analysis for Environmental Management of Groundwater Contamination Sites (2014) — Velimir V. Vesselinov, Daniel O'Malley, Danny Katzman — Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Modeling, and Analysis (ISUMA)
Abstract
In contrast to many other engineering fields, the uncertainties in subsurface processes (e.g., fluid flow and contaminant transport in aquifers) and their parameters are notoriously difficult to observe, measure, and characterize. This causes severe uncertainties that need to be addressed in any decision analysis related to optimal management and remediation of groundwater contamination sites. Furthermore, decision analyses typically rely heavily on complex data analyses and/or model predictions, which are often poorly constrained as well. Recently, we have developed a model-driven decisionsupport framework (called MADS; http://mads.lanl.gov) for the management and remediation of subsurface contamination sites in which severe uncertainties and complex physics-based models are coupled to perform scientifically defensible decision analyses. The decision analyses are based on Information Gap Decision Theory (IGDT). We demonstrate the MADS capabilities by solving a decision problem related to optimal monitoring network design.
Inverse Modeling of Subsurface Flow and Transport Properties: A Review with New Developments (2008) — Jasper A. Vrugt et al. — Vadose Zone Journal
Abstract
Many of the parameters in subsurface flow and transport models cannot be estimated directly at the scale of interest, but can only be derived through inverse modeling. During this process, the parameters are adjusted in such a way that the behavior of the model approximates, as closely and consistently as possible, the observed response of the system under study for some historical period of time. We briefly review the current state of the art of inverse modeling for estimating unsaturated flow and transport processes. We summariz how the inverse method works, discuss the historical background that led to the current perspectives on inverse modeling, and review the solution algorithms used to solve the parameter estimation problem. We then highlight our recent work at Los Alamos related to the development and implementation of improved optimization and data assimilation methods for computationally efficient calibration and uncertainty estimation in complex, distributed flow and transport models using parallel computing capabilities. Finally, we illustrate these developments with three different case studies, including (i) the calibration of a fully coupled three‐dimensional vapor extraction model using measured concentrations of volatile organic compounds in the subsurface near the Los Alamos National Laboratory, (ii) the multiobjective inverse estimation of soil hydraulic properties in the HYDRUS‐1D model using observed tensiometric data from an experimental field plot in New Zealand, and (iii) the simultaneous estimation of parameter and states in a groundwater solute mixture model using data from a multitracer experiment at Yucca Mountain, Nevada.

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MADS is an open-source software framework providing cutting-edge methods and tools for data analyses and model diagnostics.

MADS can be coupled with any model. The analyzed models can represent any physics, including hydrological, environmental, and climate models. They can be numerical, analytical, or ML-developed models. Efficient parallel computing is supported for analyses of large-scale models.

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Related publications

A computationally efficient parallel <scp>L</scp>evenberg‐<scp>M</scp>arquardt algorithm for highly parameterized inverse model analyses (2016) — Youzuo Lin, Daniel O'Malley, Velimir V. Vesselinov — Water Resources Research
Abstract
Abstract Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg‐Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg‐Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large‐scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2‐D and a random hydraulic conductivity field in 3‐D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework ( http://mads.lanl.gov ). By comparing with Levenberg‐Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg‐Marquardt method yields a speed‐up ratio on the order of to in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large‐scale problems.
Robust Decision Analysis for Environmental Management of Groundwater Contamination Sites (2014) — Velimir V. Vesselinov, Daniel O'Malley, Danny Katzman — Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Modeling, and Analysis (ISUMA)
Abstract
In contrast to many other engineering fields, the uncertainties in subsurface processes (e.g., fluid flow and contaminant transport in aquifers) and their parameters are notoriously difficult to observe, measure, and characterize. This causes severe uncertainties that need to be addressed in any decision analysis related to optimal management and remediation of groundwater contamination sites. Furthermore, decision analyses typically rely heavily on complex data analyses and/or model predictions, which are often poorly constrained as well. Recently, we have developed a model-driven decisionsupport framework (called MADS; http://mads.lanl.gov) for the management and remediation of subsurface contamination sites in which severe uncertainties and complex physics-based models are coupled to perform scientifically defensible decision analyses. The decision analyses are based on Information Gap Decision Theory (IGDT). We demonstrate the MADS capabilities by solving a decision problem related to optimal monitoring network design.
Inverse Modeling of Subsurface Flow and Transport Properties: A Review with New Developments (2008) — Jasper A. Vrugt et al. — Vadose Zone Journal
Abstract
Many of the parameters in subsurface flow and transport models cannot be estimated directly at the scale of interest, but can only be derived through inverse modeling. During this process, the parameters are adjusted in such a way that the behavior of the model approximates, as closely and consistently as possible, the observed response of the system under study for some historical period of time. We briefly review the current state of the art of inverse modeling for estimating unsaturated flow and transport processes. We summariz how the inverse method works, discuss the historical background that led to the current perspectives on inverse modeling, and review the solution algorithms used to solve the parameter estimation problem. We then highlight our recent work at Los Alamos related to the development and implementation of improved optimization and data assimilation methods for computationally efficient calibration and uncertainty estimation in complex, distributed flow and transport models using parallel computing capabilities. Finally, we illustrate these developments with three different case studies, including (i) the calibration of a fully coupled three‐dimensional vapor extraction model using measured concentrations of volatile organic compounds in the subsurface near the Los Alamos National Laboratory, (ii) the multiobjective inverse estimation of soil hydraulic properties in the HYDRUS‐1D model using observed tensiometric data from an experimental field plot in New Zealand, and (iii) the simultaneous estimation of parameter and states in a groundwater solute mixture model using data from a multitracer experiment at Yucca Mountain, Nevada.