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  1. Abstract

    Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2plume predictions near, and far away, from the monitoring wells.

     
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  2. We present the Seismic Laboratory for Imaging and Modeling/Monitoring open-source software framework for computational geophysics and, more generally, inverse problems involving the wave equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, the software is designed to be both readable and scalable, allowing researchers to easily formulate problems in an abstract fashion while exploiting the latest developments in high-performance computing. The design principles and their benefits are illustrated and demonstrated by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which, aside from coupling of wave physics and multiphase flow, involves machine learning. 
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    Free, publicly-accessible full text available July 1, 2024
  3. Abstract. Many applications in science require that computational models and data becombined. In a Bayesian framework, this is usually done by defininglikelihoods based on the mismatch of model outputs and data. However,matching model outputs and data in this way can be unnecessary or impossible.For example, using large amounts of steady state data is unnecessary becausethese data are redundant. It is numerically difficult to assimilate data inchaotic systems. It is often impossible to assimilate data of a complexsystem into a low-dimensional model. As a specific example, consider alow-dimensional stochastic model for the dipole of the Earth's magneticfield, while other field components are ignored in the model. The aboveissues can be addressed by selecting features of the data, and defininglikelihoods based on the features, rather than by the usual mismatch of modeloutput and data. Our goal is to contribute to a fundamental understanding ofsuch a feature-based approach that allows us to assimilate selected aspectsof data into models. We also explain how the feature-based approach can beinterpreted as a method for reducing an effective dimension and derive newnoise models, based on perturbed observations, that lead to computationallyefficient solutions. Numerical implementations of our ideas are illustratedin four examples.

     
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