17 papers · ranked by Valyu relevance
Alain Oliviero-Durmus, Yazid Janati, Eric Moulines, Marcelo Pereyra + 1 more
'Sebastian Reich'] This special issue addresses Bayesian inverse problems using data-driven priors derived from deep generative models (DGMs) and the convergence of generative modelling techniques and Bayesian inference methods. Conventional Bayesian priors often fail to accurately capture the properties and the…
EVAN SCOPE CRAFTS, UMBERTO VILLA
In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate a diffusion model trained on the prior distribution with a given likelihood…
Julianne Chung, Scot M. Miller, Malena Sabate Landman, Arvind K. Saibaba
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive Gaussian noise and Gaussian priors defined using Matérn covariance models. In this…
Pierre Kerfriden, Abhishek Kundu, Susanne Claus
The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result.…
Dong Yan, Shota Gugushvili, Aad van der Vaart
We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration…
Michael Sinsbeck, Marvin Höge, Wolfgang Nowak
Methods for sequential design of computer experiments typically consist of two phases. In the first phase, the exploratory phase, a space-filling initial design is used to estimate hyperparameters of a Gaussian process emulator (GPE) and to provide some initial global exploration of the model function. In the second…
Jean-Charles Croix, Nicolas Durrande, Mauricio A. Alvarez
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging or ill-posed.…
Qin Li, Kit Newton
Optical tomography is the process of reconstructing the optical properties of biological tissue using measurements of incoming and outgoing light intensity at the tissue boundary. Mathematically, light propagation is modeled by the radiative transfer equation (RTE), and optical tomography amounts to reconstructing the…
Ali Mohammad-Djafari, Wolfgang von der Linden, Sascha Ranftl
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed.…
Vikas R. Bhat, Basudha Pal, H. Anitha, Ananthakrishna Thalengala
In this paper, the inverse problems of cardiac sources using analytical and probabilistic methods are solved and discussed. The standard Tikhonov regularization technique is solved initially to estimate the under-determined heart surface potentials from Magnetocardiographic (MCG) signals. The results of the…
Guillermo Rus, Juan Melchor
Optimizing an experimental design is a complex task when a model is required for indirect reconstruction of physical parameters from the sensor readings. In this work, a formulation is proposed to unify the probabilistic reconstruction of mechanical parameters and an optimization problem. An information-theoretic…
Danny Smyl, Andreas Hauptmann, Tyler Tallman
1. ## Introduction Inverse problems have always been about peering through a mirror-looking backwards from the things we can measure to learn about the things we cannot directly see. In the last few years, that mirror has been polished by faster algorithms, smarter statistics and a new ally in machine learning. In the…
Natalya Denisova
The Bayesian approach Maximum a Posteriori (MAP) provides a common basis for developing statistical methods for solving ill-posed image reconstruction problems. MAP solutions are dependent on a priori model. Approaches developed in literature are based on prior models that describe the properties of the expected image…
Yosra Marnissi, Emilie Chouzenoux, Amel Benazza-Benyahia, Jean-Christophe Pesquet
'Jean-Christophe Pesquet'] In this paper, we are interested in Bayesian inverse problems where either the data fidelity term or the prior distribution is Gaussian or driven from a hierarchical Gaussian model. Generally, Markov chain Monte Carlo (MCMC) algorithms allow us to generate sets of samples that are employed to…
Alex Glyn-Davies, Arnaud Vadeboncoeur, O. Deniz Akyildiz, Ieva Kazlauskaite + 1 more
'Ieva Kazlauskaite' 'Mark Girolami'] Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its…
Timothy Rumbell, Jaimit Parikh, James Kozloski, Viatcheslav Gurev
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g. ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MMs). Two classes of methodologies, based on Bayesian…
Shima Kamyab, Zohreh Azimifar, Rasool Sabzi, Paul Fieguth + 1 more
In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare…