unpublished.bib

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@UNPUBLISHED{gahlot2024uads,
  author = {Abhinav Prakash Gahlot and Rafael Orozco and Ziyi Yin and Felix J. Herrmann},
  title = {An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring},
  year = {2024},
  month = {10},
  abstract = {As a society, we are faced with important challenges to combat climate change. Geological Carbon Storage (GCS), during which gigatonnes of super-critical CO2 are stored underground, is arguably the only scalable net-negative CO2-emission technology that is available. While promising, subsurface complexities and heterogeneity of reservoir properties demand a systematic approach to quantify uncertainty when optimizing production and mitigating storage risks, which include assurances of Containment and Conformance of injected supercritical CO2. As a first step towards the design and implementation of a Digital Twin for monitoring and control of underground storage operations, a machine-learning-based data-assimilation framework is introduced and validated on carefully designed realistic numerical simulations. Because our implementation is based on Bayesian inference, but does not yet support control and decision-making, we coin our approach an uncertainty-aware Digital Shadow. To characterize the posterior distribution for the state of CO2 plumes (its CO2 concentration and pressure), conditioned on multi-modal time-lapse data, the envisioned Shadow combines techniques from Simulation-Based Inference (SBI) and Ensemble Bayesian Filtering to establish probabilistic baselines and assimilate multi-modal data for GCS problems that are challenged by large degrees of freedom, nonlinear multiphysics, non-Gaussianity, and computationally expensive to evaluate fluid-flow and seismic simulations. To enable SBI for dynamic systems, a recursive scheme is proposed where the Digital Shadow’s neural networks are trained on simulated ensembles for their state and observed data (well and/or seismic). Once training is completed, the system’s state is inferred when time-lapse field data becomes available. Contrary to ensemble Kalman filtering, corrections to the predicted simulated states are not based on linear updates, but instead follow during the Analysis step of Bayesian filtering from a prior-to-posterior mapping through the latent space of a nonlinear transform. Starting from a probabilistic model for the permeability field, derived from a baseline surface-seismic survey, the proposed Digital Shadow is validated on unseen simulated ground-truth time-lapse data. In this computational study, we observe that a lack of knowledge on the permeability field can be factored into the Digital Shadow’s uncertainty quantification. Our results also indicate that the highest reconstruction quality is achieved when the state of the CO2 plume is conditioned on both time-lapse seismic data and wellbore measurements. Despite the incomplete knowledge of the permeability field, the proposed Digital Shadow was able to accurately track the unseen physical state of the subsurface throughout the duration of a realistic CO2 injection project. To the best of our knowledge, this work represents the first proof-of-concept of an uncertainty-aware, in-principle scalable, Digital Shadow that captures the uncertainty arising from unknown reservoir properties and noisy observations. This framework provides a foundation for the development of a Digital Twin aimed at mitigating risks and optimizing the management of underground storage projects.},
  keywords = {GCS, digital twin, sequential Bayes, conditional normalizing flows, Bayesian inference, uncertainty quantification, deep learning, inverse problems, summary statistics},
  url = {https://slim.gatech.edu/Publications/Public/Submitted/2024/gahlot2024uads/paper.html},
  doi = {10.48550/arXiv.2410.01218},
}

@UNPUBLISHED{bruer2024smpd,
  author = {Grant Bruer and Abhinav Prakash Gahlot and Edmond Chow and Felix J. Herrmann},
  title = {Seismic monitoring of CO2 plume dynamics using ensemble Kalman filtering},
  year = {2024},
  month = {9},
  abstract = {Monitoring carbon dioxide (CO2) injected and stored in subsurface reservoirs is critical for avoiding failure scenarios and enables real-time optimization of CO2 injection rates. Sequential Bayesian data assimilation (DA) is a statistical method for combining information over time from multiple sources to estimate a hidden state, such as the spread of the subsurface CO2 plume. An example of scalable and efficient sequential Bayesian DA is the ensemble Kalman filter (EnKF). We improve upon existing DA literature in the seismic-CO2 monitoring domain by applying this scalable DA algorithm to a high-dimensional CO2 reservoir using two-phase flow dynamics and time-lapse full waveform seismic data with a realistic surface-seismic survey design. We show more accurate estimates of the CO2 saturation field using the EnKF compared to using either the seismic data or the fluid physics alone. Furthermore, we test a range of values for the EnKF hyperparameters and give guidance on their selection for seismic CO2 reservoir monitoring.},
  keywords = {GCS, Ensebmle Kalman Filter, non-linear dynamical systems, seismic, inverse problems},
  doi = {10.48550/arXiv.2409.05193},
}

@UNPUBLISHED{orozco2024IPaspire,
  author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann},
  title = {ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems},
  year = {2024},
  month = {5},
  abstract = {Due to their uncertainty quantification, Bayesian solutions to
inverse problems are the framework of choice in applications that are risk
averse. These benefits come at the cost of computations that are in general,
intractable. New advances in machine learning and variational inference (VI)
have lowered the computational barrier by learning from examples. Two VI
paradigms have emerged that represent different tradeoffs: amortized and
non-amortized. Amortized VI can produce fast results but due to generalizing
to many observed datasets it produces suboptimal inference results.
Non-amortized VI is slower at inference but finds better posterior
approximations since it is specialized towards a single observed dataset.
Current amortized VI techniques run into a sub-optimality wall that can not
be improved without more expressive neural networks or extra training data.
We present a solution that enables iterative improvement of amortized
posteriors that uses the same networks architectures and training data. The
benefits of our method requires extra computations but these remain frugal
since they are based on physics-hybrid methods and summary statistics.
Importantly, these computations remain mostly offline thus our method
maintains cheap and reusable online evaluation while bridging the
approximation gap these two paradigms. We denote our proposed method
ASPIRE - Amortized posteriors with Summaries that are
Physics-based and Iteratively REfined. We first validate our
method on a stylized problem with a known posterior then demonstrate its
practical use on a high-dimensional and nonlinear transcranial medical
imaging problem with ultrasound. Compared with the baseline and previous
methods from the literature our method stands out as an computationally
efficient and high-fidelity method for posterior inference.},
  keywords = {Normalizing flows, amortization gap, Bayesian inference, simulation-based inference, amortized variational inference, medical imaging},
  doi = {10.48550/arXiv.2405.05398}
}