Related papers: Bayesian Inversion, Uncertainty Analysis and Inter…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations.…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…
Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so.…
Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…