@article{cockett2015,
title = {SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications},
journal = {Computers & Geosciences},
volume = {85},
pages = {142-154},
year = {2015},
issn = {0098-3004},
doi = {https://doi.org/10.1016/j.cageo.2015.09.015},
url = {https://www.sciencedirect.com/science/article/pii/S009830041530056X},
author = {Rowan Cockett and Seogi Kang and Lindsey J. Heagy and Adam Pidlisecky and Douglas W. Oldenburg},
keywords = {Geophysics, Numerical modeling, Inversion, Electromagnetics, Sensitivities, Object-oriented programming},
abstract = {Inverse modeling is a powerful tool for extracting information about the subsurface from geophysical data. Geophysical inverse problems are inherently multidisciplinary, requiring elements from the relevant physics, numerical simulation, and optimization, as well as knowledge of the geologic setting, and a comprehension of the interplay between all of these elements. The development and advancement of inversion methodologies can be enabled by a framework that supports experimentation, is flexible and extensible, and allows the knowledge generated to be captured and shared. The goal of this paper is to propose a framework that supports many different types of geophysical forward simulations and deterministic inverse problems. Additionally, we provide an open source implementation of this framework in Python called SimPEG (Simulation and Parameter Estimation in Geophysics, http://simpeg.xyz). Included in SimPEG are staggered grid, mimetic finite volume discretizations on a number of structured and semi-structured meshes, convex optimization programs, inversion routines, model parameterizations, useful utility codes, and interfaces to standard numerical solver packages. The framework and implementation are modular, allowing the user to explore, experiment with, and iterate over a variety of approaches to the inverse problem. SimPEG provides an extensible, documented, and well-tested framework for inverting many types of geophysical data and thereby helping to answer questions in geoscience applications. Throughout the paper we use a generic direct current resistivity problem to illustrate the framework and functionality of SimPEG.}
}

@article{heagy2017,
title = {A framework for simulation and inversion in electromagnetics},
journal = {Computers & Geosciences},
volume = {107},
pages = {1-19},
year = {2017},
issn = {0098-3004},
doi = {https://doi.org/10.1016/j.cageo.2017.06.018},
url = {https://www.sciencedirect.com/science/article/pii/S0098300416303946},
author = {Lindsey J. Heagy and Rowan Cockett and Seogi Kang and Gudni K. Rosenkjaer and Douglas W. Oldenburg},
keywords = {Geophysics, Numerical modelling, Finite volume, Sensitivities, Object oriented},
abstract = {Simulations and inversions of electromagnetic geophysical data are paramount for discerning meaningful information about the subsurface from these data. Depending on the nature of the source electromagnetic experiments may be classified as time-domain or frequency-domain. Multiple heterogeneous and sometimes anisotropic physical properties, including electrical conductivity and magnetic permeability, may need be considered in a simulation. Depending on what one wants to accomplish in an inversion, the parameters which one inverts for may be a voxel-based description of the earth or some parametric representation that must be mapped onto a simulation mesh. Each of these permutations of the electromagnetic problem has implications in a numerical implementation of the forward simulation as well as in the computation of the sensitivities, which are required when considering gradient-based inversions. This paper proposes a framework for organizing and implementing electromagnetic simulations and gradient-based inversions in a modular, extensible fashion. We take an object-oriented approach for defining and organizing each of the necessary elements in an electromagnetic simulation, including: the physical properties, sources, formulation of the discrete problem to be solved, the resulting fields and fluxes, and receivers used to sample to the electromagnetic responses. A corresponding implementation is provided as part of the open source simulation and parameter estimation project SimPEG (http://simpeg.xyz). The application of the framework is demonstrated through two synthetic examples and one field example. The first example shows the application of the common framework for 1D time domain and frequency domain inversions. The second is a field example that demonstrates a 1D inversion of electromagnetic data collected over the Bookpurnong Irrigation District in Australia. The final example is a 3D example which shows how the modular implementation is used to compute the sensitivity for a parametric model where a transmitter is positioned inside a steel cased well.}
}

@Book{economic-dynamics-book,
  author={John Stachurski},
  title={{Economic Dynamics: Theory and Computation}},
  publisher={The MIT Press},
  year=2009,
  month={December},
  volume={1},
  number={0262012774},
  series={MIT Press Books},
  edition={},
  keywords={economic dynamics; nonlinear dynamic systems; Markov chains; programming},
  doi={},
  isbn={ARRAY(0x4dac6e08)},
  abstract={This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real world problems. The material makes extensive use of programming examples to illustrate ideas. These programs help bring to life the abstract concepts in the text. Background in computing and analysis is offered for readers without programming experience or upper-level mathematics. Topics covered in detail include nonlinear dynamic systems, finite state Markov chains, stochastic dynamic programming, and stochastic stability and computation of equilibria. The models are predominantly nonlinear, and the emphasis is on studying nonlinear systems in their original form, rather than by means of rudimentary approximation methods such as linearization. Much of the material is new to economics and improves on existing techniques. For graduate students and those already working in the field, Economic Dynamics will serve as an essential resource.},
  url={https://ideas.repec.org/b/mtp/titles/0262012774.html}
}