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Composing Normalizing Flows for Inverse Problems
[article]
2021
arXiv
pre-print
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Our method is evaluated on a variety of inverse problems and is shown to produce high-quality samples with uncertainty quantification. ...
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. ...
Acknowledgements This research has been supported by NSF Grants CCF 1934932, AF 1901292, 2008710, 2019844 the NSF IFML 2019844 award as well as research gifts by Western Digital, WNCG and MLL, computing resources from ...
arXiv:2002.11743v3
fatcat:nwrjrh6wgbggdls4ttqj4w2y7a
Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization
[article]
2020
arXiv
pre-print
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Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting ...
We validate these ideas with an application to angle-versus-ray parameter analysis for reservoir characterization. ...
The solution of problem (15) comes in the form of a network G θ , whose evaluation over random z's generates models m's as if they were sampled from the posterior distribution in Equation (3) . ...
arXiv:2004.07871v1
fatcat:3vnq27hmobeljiikrt7e4yvcte
Inverse design of two-dimensional materials with invertible neural networks
[article]
2021
arXiv
pre-print
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To tackle this problem, we propose an inverse design framework (MatDesINNe) utilizing invertible neural networks which can map both forward and reverse processes between the design space and target property ...
This approach can be used to generate materials candidates for a designated property, thereby satisfying the highly sought-after goal of inverse design. ...
and to efficiently "close the loop" between modelling and experiments. 4, 15, 16, 17, 18 In general inverse problems, given a forward process y = f(x), the goal is to then find a suitable inverse model ...
arXiv:2106.03013v1
fatcat:a2ktq3p4angt5j2q7im3r5j6m4
Analyzing Inverse Problems with Invertible Neural Networks
[article]
2019
arXiv
pre-print
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While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables ...
Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. ...
Hence we want to express the inverse model as a conditional probability p(x | y), but its mathematical derivation from the forward model is intractable in the applications we are going to address. ...
arXiv:1808.04730v3
fatcat:flnbezu3q5akxbqlqzgrdnzi3q
Conditional Invertible Neural Networks for Medical Imaging
2021
Journal of Imaging
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In our work, we apply generative flow-based models based on invertible neural networks to two challenging medical imaging tasks, i.e., low-dose computed tomography and accelerated medical resonance imaging ...
Over recent years, deep learning methods have become an increasingly popular choice for solving tasks from the field of inverse problems. ...
Application of Generative Models to Inverse Problems Inverse problems can be studied from a statistical point of view [8] . ...
doi:10.3390/jimaging7110243
pmid:34821874
pmcid:PMC8624162
fatcat:sjwz7w6jdvdthmf7fs32ifstyu
Solving inverse problems using conditional invertible neural networks
[article]
2020
arXiv
pre-print
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In this work, we construct a two- and three-dimensional inverse surrogate models consisting of an invertible and a conditional neural network trained in an end-to-end fashion with limited training data ...
The invertible network is developed using a flow-based generative model. ...
Here, we train the cINN model with varying length-scales instead of training the model with a constant length scale (this will allow us to solve inverse problems with true log-permeabilities sampled from ...
arXiv:2007.15849v1
fatcat:jcypzoaxavdsxplmcsje6k6sye
Strategies for integrating uncertainty in iterative geostatistical seismic inversion
[article]
2018
arXiv
pre-print
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A single geostatistical framework is proposed and illustrated with its application to a real case study. ...
Local PDFs are used as conditioning data to a stochastic sequential simulation algorithm, included as the model perturbation within the inversion. ...
It is an ill-posed, nonlinear inverse problem with multiple solutions: many different elastic models can lead to the generation of highly similar synthetic responses that match considerably well the observed ...
arXiv:1810.07405v1
fatcat:orkkyeypjrgotmqqsigglgdi5i
Direct Hydraulic Parameter and Function Estimation for Diverse Soil Types Under Infiltration and Evaporation
2016
Transport in Porous Media
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Unlike the traditional indirect inversion method, the direct method does not require forward simulations to assess the measurement-to-model fit; thus, the knowledge of model boundary conditions (BC) is ...
Instead, the method employs a set of local approximate solutions to impose continuity of pressure head and soil water fluxes throughout the inversion domain, while measurements act to condition these solutions ...
Therefore, for the general applications of our approach, we can invert reasonable K(ψ) for any observed pressure heads. ...
doi:10.1007/s11242-016-0801-0
fatcat:nzthczphz5bvnj6j2oyvxo4a3e
Metamodel Based Forward and Inverse Design for Passive Vibration Suppression
[article]
2020
arXiv
pre-print
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A suite of neural networks (ANN) is trained on TMM samples (which present minute-scale computing costs per evaluation), to model the frequency response. ...
Further novel contribution occurs through the development of an inverse modeling approach that can instantaneously produce the 1D metamaterial design with minimum mass for a given desired non-resonant ...
Inverse Design As mentioned earlier, the INN was trained on samples generated from optimization. ...
arXiv:2007.15038v1
fatcat:xltb4reibfdt5iwbqfpsim2s7m
Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows
[article]
2020
arXiv
pre-print
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We then train another invertible generator with output density q'_ϕ(x|y') specifically for y', allowing us to sample from the posterior p_X|Y'(x|y'). ...
In inverse problems, we often have access to data consisting of paired samples (x,y)∼ p_X,Y(x,y) where y are partial observations of a physical system, and x represents the unknowns of the problem. ...
The examples here considered are encouraging for seismic or optoacoustic imaging applications, but additional challenges are expected for large scales due to the high dimensionality of the solution and ...
arXiv:2007.07985v1
fatcat:eraddlxs3vdangqzziykadcuue
Conditional Normalizing Flows for Low-Dose Computed Tomography Image Reconstruction
[article]
2020
arXiv
pre-print
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Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated. ...
To tackle this problem, we propose a hybrid conditional normalizing flow, which integrates the physical model by using the filtered back-projection as conditioner. ...
Johannes Leuschner and Maximilian Schmidt acknowledge the support by the Deutsche Forschungsgemeinschaft (DFG) within the framework of GRK 2224/1 "π 3 : Parameter Identification -Analysis, Algorithms, Applications ...
arXiv:2006.06270v1
fatcat:z24grd3rxzghhmxj4if3vnbgoi
Benchmarking deep inverse models over time, and the neural-adjoint method
[article]
2021
arXiv
pre-print
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Finally, inspired by our conception of the inverse problem, we explore a solution that uses a deep learning model to approximate the forward model, and then uses backpropagation to search for good inverse ...
We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. ...
During inference phase, inverse solution x is decoded from random samples are drawn from z space conditioned on y. ...
arXiv:2009.12919v4
fatcat:qgrznk47eveffhds26dmlhwapm
Multi-scale uncertainty quantification in geostatistical seismic inversion
[article]
2018
arXiv
pre-print
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This assumption leads to underestimation of the uncertainty associated with the inverted models. ...
The framework couples geostatistical seismic inversion with a stochastic adaptive sampling and Bayesian inference of the metaparameters to provide a more accurate and realistic prediction of uncertainty ...
generated from the mean Ip model computed from the iteration with lowest misfit. ...
arXiv:1810.03919v1
fatcat:lk5nhwbrnfc6tnmqqwv7zc6gvi
Deep Neural Networks are Surprisingly Reversible: A Baseline for Zero-Shot Inversion
[article]
2021
arXiv
pre-print
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Analysis can be performed via reversing the network's flow to generate inputs from internal representations. ...
The crux of our method is to inverse the DNN in a divide-and-conquer manner while re-syncing the inverted layers via cycle-consistency guidance with the help of synthesized data. ...
The method is applicable to discriminative (Sec. 4.1) and generative (Sec. 4.2) models trained on complex datasets. ...
arXiv:2107.06304v1
fatcat:ohamubvcjffxdlbe7sbioxpu2y
Conditional Recurrent Flow: Conditional Generation of Longitudinal Samples With Applications to Neuroimaging
2019
2019 IEEE/CVF International Conference on Computer Vision (ICCV)
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We develop a conditional generative model for longitudinal image datasets based on sequential invertible neural networks. ...
The key goal is not only to estimate the parameters of a deep generative model for the given longitudinal data, but also to enable evaluation of how the temporal course of the generated longitudinal samples ...
Conditional Sample Generation Naturally, an inverse problem can be posed as a sample generation procedure by sampling a latent variable z and inverse mapping it to x = f −1 (z), thus generating a new sample ...
doi:10.1109/iccv.2019.01079
pmid:32405276
pmcid:PMC7220239
fatcat:er4w4nv7xjcf5dpsb5bfahmake
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