Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification

Orozco, Rafael; Siahkoohi, Ali; Rizzuti, Gabrio; Leeuwen, Tristan van; Herrmann, Felix J.

doi:10.1117/12.2651691

Cited by 5 publications

(1 citation statement)

References 65 publications

(85 reference statements)

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“…Transcranial ultrasound computed tomography (USCT) is an emerging imaging modality which relies on transmitting ultrasound waves through the skull in order to recover reconstructions of the interior brain tissue. [1][2][3][4] This area of research has garnered significant interest in recent years given its ability to serve as an alternative to computed tomography (CT) or magnetic resonance imaging (MRI) for diagnosing and monitoring brain-related ailments.…”

Section: Introductionmentioning

confidence: 99%

Towards elastic bone characterization in transcranial ultrasound

Marty,

Mitcham,

Ali

et al. 2024

Medical Imaging 2024: Ultrasonic Imaging and Tomography

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Constructing a physics-augmented digital twin of the skull is imperative for a wide range of transcranial ultrasound applications including ultrasound computed tomography and focused ultrasound therapy. The high impedance contrast as well as the acoustic-elastic coupling observed between soft tissue and bone increase the complexity of the ultrasound wavefield considerably, thus emphasizing the need for waveform-based inversion approaches. This work applies reverse time migration in conjunction with the spectral-element method to an in vitro human skull to obtain a starting model, which can be used for full-waveform inversion and adjoint-based shape optimization. Two distinct brain phantoms are considered where the cranial cavity of the in vitro human skull was filled with (1) homogeneous water and (2) gelatin with two cylindrical inclusions. A 2D slice through the posterior of the skull was collected using a ring-like aperture consisting of 1024 ultrasound transducers with a bandwidth of approximately 1 MHz to 3 MHz. Waveform-based reverse time migration was then used to resolve the inner and outer contours of the skull from which a conforming hexahedral finite-element mesh was constructed. The synthetically generated measurements which are obtained by solving the coupled acousticviscoelastic wave equation are in good agreement with the observed laboratory measurements. It is demonstrated that using this revised wave speed model for recomputing the reverse time migration reconstructions allows for improved localization of the gelatin inclusions within the cranial cavity.

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Section: Introductionmentioning

confidence: 99%

Towards elastic bone characterization in transcranial ultrasound

Marty,

Mitcham,

Ali

et al. 2024

Medical Imaging 2024: Ultrasonic Imaging and Tomography

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show abstract

Solving multiphysics-based inverse problems with learned surrogates and constraints

Yin,

Orozco,

Louboutin

et al. 2023

Adv. Model. and Simul. in Eng. Sci.

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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 CO2 plume predictions near, and far away, from the monitoring wells.

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Reliable amortized variational inference with physics-based latent distribution correction

Siahkoohi

Rizzuti²,

Orozco

et al. 2023

GEOPHYSICS

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Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges by pretraining a neural network that acts as a surrogate conditional distribution that approximates the posterior distribution not only for one instance of the observed data but also for the distribution of the data pertaining to a specific inverse problem. When fed previously unseen data, the neural network — in our case, a conditional normalizing flow — provides the posterior samples at virtually no cost. However, the accuracy of amortized variational inference relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the earth’s heterogeneous subsurface. In addition, the network is prone to errors if evaluated over data that are not drawn from the training data distribution. As such, we have aimed to increase the resilience of amortized variational inference in the presence of moderate data distribution shifts. We achieve this via a correction to the conditional normalizing flow’s latent distribution that improves the approximation to the posterior distribution for the data at hand. The correction involves relaxing the standard Gaussian assumption on the latent distribution and parameterizing it via a Gaussian distribution with an unknown mean and (diagonal) covariance. These unknowns are then estimated by minimizing the Kullback-Leibler divergence between the corrected and the (physics-based) true posterior distributions. Although generic and applicable to other inverse problems by means of a linearized seismic imaging example, we find that our correction step improves the robustness of amortized variational inference with respect to changes in the number of seismic sources, noise variance, and shifts in the prior distribution. This approach, given noisy seismic data simulated via the linearized Born modeling, provides a seismic image with limited artifacts and an assessment of its uncertainty at approximately the same cost as five reverse time migrations.

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Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification

Cited by 5 publications

References 65 publications

Towards elastic bone characterization in transcranial ultrasound

Towards elastic bone characterization in transcranial ultrasound

Solving multiphysics-based inverse problems with learned surrogates and constraints

Reliable amortized variational inference with physics-based latent distribution correction

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