25 papers · ranked by Valyu relevance
Jasper Marijn Everink, Chao Zhang, Amal Alghamdi, Rémi Laumont + 2 more
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are commonly used, but they require prior and likelihood densities to be explicitly…
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…
Zhiliang Deng, Zhiyuan Wang, Xiaomei Yang, Xiaofei Guan
We present a novel Bayesian framework for inverse problems in which the posterior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation, and the superposition property of PPPs is then exploited to enable efficient…
D. Andrew Brown, Arvind K. Saibaba, Sarah Vallélian
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution. However, implementations of such algorithms can be computationally expensive. We…
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…
Horst, Andreas, Afkham, Babak Maboudi + 4 more
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov priors are discretization invariant and can promote sparsity in terms of wavelet…
Dhruv Patel, Deep Ray, Assad A. Oberai
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is tackling their ill-posed nature. Bayesian inference provides a principled approach…
Junxiong Jia, Qianchuan Zhao, Zongben Xu, Deyu Meng + 1 more
Bayesian approach, a useful tool for quantifying uncertainties, has been extensively employed to solve the inverse problems of partial differential equations (PDEs). One of the main difficulties in employing the Bayesian approach to such problems is how to extract information from the posterior probability measure.…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
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.…
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…
Martin Robinson, Alan Bond, Alexandr Simonov, Jie Zhang + 1 more
Recently, we have introduced the use of techniques drawn from Bayesian statistics to recover kinetic and thermodynamic parameters from voltammetric data, and were able to show that the technique of large amplitude ac voltammetry yielded significantly more accurate parameter values than the equivalent dc approach. In…
Anuja Negi, Stefan Haufe, Alexandre Gramfort, Ali Hashemi
Brain source imaging (BSI), also known as source localization, from magneto- and electroencephalographic (M/EEG) data, is a challenging ill-posed inverse problem. Accurate source estimation is sensitive to modeling parameters, such as regularization strength and noise level, where misconfigurations can lead to under-…
Authors not listed
The political, social and economic consequences of climate change drastically influence the requirements of modern energy systems and its components. This includes not only energy production but also concepts and innovations for its storage, especially in magnitudes of gigawatt hours. Carnot batteries, which convert…
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…
Alberto Sorrentino, Michele Piana
We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for…
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…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Ali Hashemi, Chang Cai, Yijing Gao, Sanjay Ghosh + 3 more
We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Jürgen Köfinger, Gerhard Hummer
The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Ben Lambert, David J. Gavaghan, Simon Tavener
Biological systems have evolved a degree of robustness with respect to perturbations in their environment and this capability is essential for their survival. In applications ranging from therapeutics to conservation, it is important to understand not only the sensitivity of biological systems to changes in their…
Tianfan Jin, Brett M Savoie
Contemporary machine learning algorithms have largely succeeded in automating the development of mathematical models from data. Although this is a striking accomplishment, it leaves unaddressed the multitude of scenarios, especially across the chemical sciences and engineering, where deductive, rather than inductive…