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Results: 30
Efficient learning methods for large-scale optimal inversion design
In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where...
Bi-level learning Krylov projection methods inverse problems learning priors variational regularization /dk/atira/pure/subjectarea/asjc/2600/2606 name=Control and Optimization /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/2600/2602 name=Algebra and Number Theory
Augmented NETT regularization of inverse problems
Abstract: We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty...
Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem
Abstract
Human brain activity is based on electrochemical processes, which can only be measured invasively. Thus, quantities such as magnetic flux density (MEG) or electric...
Covid-19
In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can...
Jet noise
An exact analysis of the field radiated by tonal and random non-axisymmetric sources distributed over a disc or cylinder is presented. The analysis is exact, without recourse to near- or far-field approximations, and leads to a...
Data driven regularization by projection
Abstract: We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and...
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction...
Covid-19
In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can...
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems [M. Eigel, M....
math.NA cs.NA math.ST stat.TH 15A23 15A69 65C60 65D32 65D15 41A10 Markov Chain Monte Carlo inverse problems /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1800/1804 name=Statistics, Probability and Uncertainty /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation
Symmetrization techniques in image deblurring
This paper presents some preconditioning techniques that enhance the performance of iterative regularization methods applied to image deblurring problems determined by a wide variety of point spread functions (PSFs) and boundary...
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth
function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear
inverse problem of recovering the conductivity $f>0$ in the divergence...
Data driven regularization by projection
We study linear inverse problems under the premise that the forward operator
is not at hand but given indirectly through some input-output training pairs.
We demonstrate that regularization by projection and variational...
Energy reduction with super-resolution convolutional neural network for ultrasound tomography
Daruisz Wójcik, Tomasz Rymarczyk, Bartosz Przysucha, Michal Golabek, Dariusz Majerek, Tomasz Warowny, Manuchehr Soleimani
Feb 01, 2023
This study addresses the issue of energy optimization by investigating solutions for the reduction of energy consumption in the diagnostics and monitoring of technological processes. The implementation of advanced process...
Deep learning Energy consumption energy optimization Industry 4.0 inverse problems Machine Learning Tomography /dk/atira/pure/subjectarea/asjc/2600/2606 name=Control and Optimization /dk/atira/pure/subjectarea/asjc/2100/2101 name=Energy (miscellaneous) /dk/atira/pure/subjectarea/asjc/2200/2201 name=Engineering (miscellaneous) /dk/atira/pure/subjectarea/asjc/2100/2102 name=Energy Engineering and Power Technology /dk/atira/pure/subjectarea/asjc/2200/2208 name=Electrical and Electronic Engineering /dk/atira/pure/subjectarea/asjc/2200/2215 name=Building and Construction /dk/atira/pure/subjectarea/asjc/2100/2103 name=Fuel Technology /dk/atira/pure/subjectarea/asjc/2100/2105 name=Renewable Energy, Sustainability and the Environment /dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energy name=SDG 7 - Affordable and Clean Energy
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems [M. Eigel, M....
math.NA cs.NA math.ST stat.TH 15A23 15A69 65C60 65D32 65D15 41A10 Markov Chain Monte Carlo inverse problems /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1800/1804 name=Statistics, Probability and Uncertainty /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation
DEEP IMPORTANCE SAMPLING USING TENSOR TRAINS WITH APPLICATION TO A PRIORI AND A POSTERIORI RARE EVENTS
We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem...
Representation and reconstruction of covariance operators in linear inverse problems
Abstract
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy...
DEEP IMPORTANCE SAMPLING USING TENSOR TRAINS WITH APPLICATION TO A PRIORI AND A POSTERIORI RARE EVENTS
We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem...
Augmented NETT regularization of inverse problems
Abstract: We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty...
Iteratively Reweighted FGMRES and FLSQR for Sparse Reconstruction
This paper presents two new algorithms to compute sparse solutions of large-scale linear discrete ill-posed problems. The proposed approach consists in constructing a sequence of quadratic problems approximating an `...
Energy reduction with super-resolution convolutional neural network for ultrasound tomography
Daruisz Wójcik, Tomasz Rymarczyk, Bartosz Przysucha, Michal Golabek, Dariusz Majerek, Tomasz Warowny, Manuchehr Soleimani
Feb 01, 2023
This study addresses the issue of energy optimization by investigating solutions for the reduction of energy consumption in the diagnostics and monitoring of technological processes. The implementation of advanced process...
Deep learning Energy consumption energy optimization Industry 4.0 inverse problems Machine Learning Tomography /dk/atira/pure/subjectarea/asjc/2600/2606 name=Control and Optimization /dk/atira/pure/subjectarea/asjc/2100/2101 name=Energy (miscellaneous) /dk/atira/pure/subjectarea/asjc/2200/2201 name=Engineering (miscellaneous) /dk/atira/pure/subjectarea/asjc/2100/2102 name=Energy Engineering and Power Technology /dk/atira/pure/subjectarea/asjc/2200/2208 name=Electrical and Electronic Engineering /dk/atira/pure/subjectarea/asjc/2200/2215 name=Building and Construction /dk/atira/pure/subjectarea/asjc/2100/2103 name=Fuel Technology /dk/atira/pure/subjectarea/asjc/2100/2105 name=Renewable Energy, Sustainability and the Environment /dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energy name=SDG 7 - Affordable and Clean Energy
The difficulty of computing stable and accurate neural networks
Deep learning (DL) has had unprecedented success and is now entering
scientific computing with full force. However, current DL methods typically
suffer from instability, even when universal approximation properties guarantee
the...
A Review of Mathematical and Computational Methods in Cancer Dynamics.
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of...
Jet noise
An exact analysis of the field radiated by tonal and random non-axisymmetric sources distributed over a disc or cylinder is presented. The analysis is exact, without recourse to near- or far-field approximations, and leads to a...
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