jInv--a Flexible Julia Package for PDE Parameter Estimation

Ruthotto, Lars; Treister, Eran; Haber, Eldad

doi:10.1137/16m1081063

Cited by 38 publications

(37 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also save on latency and communication with the async-wADMM, which ran for about (16 minutes) while maintaining a good quality of the reconstruction. As expected, the joint inversions enhance the quality of the reconstruction since the different physics involved capture different properties of the model [34].…”

Section: Multiphysics Parameter Estimationsupporting

confidence: 69%

“…Although the individual terms in (11) can be computed in parallel, an efficient implementation is non-trivial. To limit the communication overhead, one can use the static scheduling approach described in [34]. Here, the model and a number of meshes, sources, receivers, and forward problems are assigned to all the workers in the offline phase.…”

Section: Numerical Optimizationmentioning

confidence: 99%

“…Here, a and b are the conductivity values set to 0.1 and 1.0 respectively, and c = 3.0 is the velocity in which the contrast is centered. More details can be found in [34]. As in Sec.…”

Section: Multiphysics Parameter Estimationmentioning

confidence: 99%

See 2 more Smart Citations

An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

Fung¹,

Ruthotto²

2019

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available workers. Since each subproblem can be associated with different forward models and right-hand-sides, this provides ample options for tailoring the method to different applications including multi-source and multi-physics PDE parameter estimation problems. We also consider an asynchronous variant of consensus ADMM to reduce communication and latency.Our key contribution is a novel weighting scheme that empirically increases the progress made in early iterations of the consensus ADMM scheme and is attractive when using a large number of subproblems. This makes consensus ADMM competitive for solving PDE parameter estimation, which incurs immense costs per iteration. The weights in our scheme are related to the uncertainty associated with the solutions of each subproblem. We exemplarily show that the weighting scheme combined with the asynchronous implementation improves the time-tosolution for a 3D single-physics and multiphysics PDE parameter estimation problems.

show abstract

Section: Multiphysics Parameter Estimationsupporting

confidence: 69%

Section: Numerical Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

Fung¹,

Ruthotto²

2019

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition to well-established software packages such as ModEM and the Aarhus Workbench (Kelbert et al, 2014;Auken et al, 2015), and existing open-source packages such as MARE2DEM (Key and Ovall, 2011), there is a growing ecosystem of open-source tools available for solving problems in electromagnetic geophysics . The open-source ecosystem also contains several other notable packages including empymod, fatiando, jInv, and py-GIMLi (Werthmüller, 2017;Uieda et al, 2013;Ruthotto et al, 2017;Rücker et al, 2017). These packages differ in objectives, capabilities, structure, interactivity, license, and coding language (commonly Python and Julia).…”

Section: Open-source Developmentmentioning

confidence: 99%

3D electromagnetic modelling and inversion: a case for open source

Oldenburg

Heagy

Kang

et al. 2019

Exploration Geophysics

View full text Add to dashboard Cite

Electromagnetics has an important role to play in solving the next generation of geoscience problems. These problems are multidisciplinary, complex, and require collaboration. This is especially true at the base scientific level where the underlying physical equations need to be solved, and data, associated with physical experiments, need to be inverted. In this paper, we present arguments for adopting an open-source methodology for geophysics and provide some background about open-source software for electromagnetics. Immediate benefits are the reduced time required to carry out research, being able to collaborate, having reproducible results, and being able to disseminate results quickly. To illustrate the use of an open-source methodology in electromagnetics, we present two challenges. The first is to simulate data from a time domain airborne system over a conductive plate buried in a more resistive earth. The second is to jointly invert airborne TDEM and FDEM data with ground TDEM. SimPEG, Simulation and Parameter Estimation in Geophysics, (https://simpeg.xyz) is used for the open-source software. The figures in this paper can be reproduced by downloading the Jupyter Notebooks we provide with this paper (https://github.com/simpegresearch/oldenburg-2018-AEM). Access to the source code allows the researcher to explore the simulations and inversions by changing model and inversion parameters, plot fields and fluxes to gain further insight about the EM phenomena, and solve a new research problem by using open-source software as a base. By providing results in a manner that allows others to reproduce, further explore, and even extend them, we hope to demonstrate that an open-source paradigm has the potential to enable more rapid progress of the geophysics community as a whole.

show abstract

“…Implementation. Our numerical framework for minimizing the empirical Bayes risk is implemented as an add-on to the parameter estimation package jInv [33]. To benefit from jInv's existing capabilities, the routines for solving the lower-level problem and computing sensitivities are implemented as a module, extending the abstract forward problem type.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Optimal Experimental Design for Inverse Problems with State Constraints

Ruthotto¹,

Chung²,

Chung³

2018

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow to reduce the experimental costs by minimizing the number of measurements. The first formulation assumes a fine discretization of the design parameter space and uses sparsity promoting regularization to obtain an efficient design. The second formulation parameterizes the design and seeks optimal placement for these measurements by solving a small-dimensional optimization problem. We consider both problems in a Bayes risk as well as an empirical Bayes risk minimization framework. For the unconstrained inverse state problem, we exploit the closed form solution for the inner problem to efficiently compute derivatives for the outer OED problem. The empirical formulation does not require an explicit solution of the inverse problem and therefore allows to integrate constraints efficiently. A key contribution is an efficient optimization method for solving the resulting, typically high-dimensional, bilevel optimization problem using derivative-based methods. To overcome the lack of non-differentiability in active set methods for inequality constraints problems, we use a relaxed interior point method. To address the growing computational complexity of empirical Bayes OED, we parallelize the computation over the training models. Numerical examples and illustrations from tomographic reconstruction, for various data sets and under different constraints, demonstrate the impact of constraints on the optimal design and highlight the importance of OED for constrained problems.

show abstract

jInv--a Flexible Julia Package for PDE Parameter Estimation

Cited by 38 publications

References 49 publications

An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

3D electromagnetic modelling and inversion: a case for open source

Optimal Experimental Design for Inverse Problems with State Constraints

Contact Info

Product

Resources

About