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Composing Normalizing Flows for Inverse Problems [article]

Jay Whang, Erik M. Lindgren, Alexandros G. Dimakis
2021 arXiv   pre-print
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations.  ...  We approach this problem as a task of conditional inference on the pre-trained unconditional flow model. We first establish that this is computationally hard for a large class of flow models.  ...  Introduction We are interested in solving inverse problems using a pretrained normalizing flow prior.  ... 
arXiv:2002.11743v3 fatcat:nwrjrh6wgbggdls4ttqj4w2y7a

Replacement of numerical simulations with machine learning in the inverse problem of two-phase flow in porous medium

Yu A Goncharova, I M Indrupskiy
2019 Journal of Physics, Conference Series  
Achieved approximation quality for the performance function on a test sample is well suitable for the inverse problem solution.  ...  A possibility to replace full-physics numerical simulations with machine-learningbased algorithms in inverse problems of multiphase flow in porous media is studied on an example of specialized oil-well  ...  Introduction Inverse problems of flow in porous media arise in many popular practical applications.  ... 
doi:10.1088/1742-6596/1391/1/012146 fatcat:dbg7kdnabvepfhgfxtiqzqadny

Generative Flows as a General Purpose Solution for Inverse Problems [article]

José A. Chávez
2022 arXiv   pre-print
We hypothesize that our approach could make generative flows a general purpose solver for inverse problems.  ...  Due to the success of generative flows to model data distributions, they have been explored in inverse problems.  ...  Each flow step is composed by an activation normalization [14] followed by our proposed coupling layer. These flow steps are combined with squeeze layers.  ... 
arXiv:2110.13285v3 fatcat:qjbljdkkoje5fetyij6u6fh7y4

Ten turbidite myths

G. Shanmugam
2002 Earth-Science Reviews  
Reality: flute structures are indicative only of flow erosion, not deposition. Myth No. 7: normal grading is a product of multiple depositional events.  ...  Reality: a reexamination of the Annot Sandstone in SE France, which served as the basis for developing the first turbidite facies model, suggests a complex depositional origin by plastic flows and bottom  ...  Kirkland for helpful suggestions, and Jean Shanmugam for editorial comments.  ... 
doi:10.1016/s0012-8252(02)00065-x fatcat:ekpafflr55gzvd2ubupcmfupbe

SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows [article]

Didrik Nielsen, Priyank Jaini, Emiel Hoogeboom, Ole Winther, Max Welling
2020 arXiv   pre-print
In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows.  ...  Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.  ...  Acknowledgements We thank Laurent Dinh and Giorgio Giannone for helpful feedback. Funding Disclosure This research was supported by the NVIDIA Corporation with the donation of TITAN X GPUs.  ... 
arXiv:2007.02731v2 fatcat:7cozym4jendrliu2jnppmpprzu

Self Normalizing Flows [article]

T. Anderson Keller, Jorn W.T. Peters, Priyank Jaini, Emiel Hoogeboom, Patrick Forré, Max Welling
2021 arXiv   pre-print
In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer.  ...  Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework.  ...  The method approximates the gradient of the log Jacobian determinant using learned inverses, allowing for the training of otherwise intractable normalizing flow architectures.  ... 
arXiv:2011.07248v2 fatcat:2v2xzvp2tzb3blaj5popop6xxe

Geometric Inversion of Two-dimensional Stokes Flows – Application to the flow between Parallel Planes

Mustapha Hellou
2010 Engineering  
Geometric inversion is applied to two-dimensional Stokes flow in the objective to find new Stokes flow solutions.  ...  Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced.  ...  For example, in the case of the flow between parallel plates, choosing this centre position on the y r axis normal to the parallel plates, provide solutions to flows around two unequal cylinders in contact  ... 
doi:10.4236/engineering.2010.210100 fatcat:iiidvn4ytrcyhkk723zxroszry

Geometric Inversion of Two-Dimensional Stokes Flows – Application to the Flow between Parallel Planes

Mustapha Hellou
2010 Engineering  
Geometric inversion is applied to two-dimensional Stokes flow in the objective to find new Stokes flow solutions.  ...  Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced.  ...  For example, in the case of the flow between parallel plates, choosing this centre position on the y r axis normal to the parallel plates, provide solutions to flows around two unequal cylinders in contact  ... 
doi:10.4236/eng.2010.210100 fatcat:ixvpusegurcg3on4xzjeum3gg4

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models [article]

Ling Guo, Hao Wu, Tao Zhou
2021 arXiv   pre-print
We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements.  ...  More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a Gaussian random field with the Karhunen-Lo\'eve (KL) expansion structure and the  ...  The second author is supported by Shanghai science and technology committee (No.20JC1413500) and the fundamental research funds for the central universities of China (No. 22120210133).  ... 
arXiv:2108.12956v2 fatcat:wxywkpvzfbavjkc2ewbcltgbum

Conditional Normalizing Flows for Low-Dose Computed Tomography Image Reconstruction [article]

Alexander Denker, Maximilian Schmidt, Johannes Leuschner, Peter Maass, Jens Behrmann
2020 arXiv   pre-print
To tackle this problem, we propose a hybrid conditional normalizing flow, which integrates the physical model by using the filtered back-projection as conditioner.  ...  Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated.  ...  Thus, conditional flows are a promising avenue for statistical model-based inverse problems such as CT reconstruction.  ... 
arXiv:2006.06270v1 fatcat:z24grd3rxzghhmxj4if3vnbgoi

Page 300 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 61, Issue 4 [page]

1955 American Mathematical Society. Bulletin of the American Mathematical Society  
Morris Morduchow: An approximate solution, by method of averages, of a differential equation for flow in a tube with normal fluid injection at wall.  ...  Venant torsion problem for such a beam the stress function or the normal derivative of the warping function must satisfy certain jump conditions on the separating boundaries.  ... 

Developing Spline Based Overset Grid Assembling Approach and Application to Unsteady Flow Around a Moving Body

Hiroshi Kobayashi, Yoshiaki Kodama
2016 Journal of Mathematics and System Science  
Flow simulation around Kriso Container Ship (KCS) with jointed grids shows good continuity of flow field between the grids.  ...  The overset grid assembling is enhanced to unsteady problem as dynamic overset approach coupled with a solver which also has been developed in National Maritime Research Institute, Japan.  ...  Acknowledgment This work has been supported by JSPS (Japan Society for the Promotion of Science) KAKENHI (Grant-in-Aid for Scientific Research) (C), Grant Number JP26420834  ... 
doi:10.17265/2159-5291/2016.09.001 fatcat:t3wei7t4yvay7jqc6ame7dhvve

ECT-LSTM-RNN: An Electrical Capacitance Tomography Model-based Long Short-Term Memory Recurrent Neural Networks for Conductive Materials

Wael Deabes, Alaa Sheta, Malik Braik
2021 IEEE Access  
This paper presents novel image reconstruction methods using Deep Learning for solving the forward and inverse problems of the ECT system for generating high-quality images of conductive materials in the  ...  the capacitance measurements collected during image reconstruction are inadequate due to the limited number of electrodes, and (3) the reconstruction process is subject to noise leading to an ill-posed problem  ...  ACKNOWLEDGMENT The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for continuous support.  ... 
doi:10.1109/access.2021.3079447 fatcat:nnkyk5wwn5d63mdgitg4kugiwu

Deep Unfolding with Normalizing Flow Priors for Inverse Problems [article]

Xinyi Wei, Hans van Gorp, Lizeth Gonzalez Carabarin, Daniel Freedman, Yonina C. Eldar, Ruud J.G. van Sloun
2022 arXiv   pre-print
State of the art methods for solving these inverse problems combine deep learning with iterative model-based solvers, a concept known as deep algorithm unfolding.  ...  In this paper, we propose to make these image priors fully explicit by embedding deep generative models in the form of normalizing flows within the unfolded proximal gradient algorithm.  ...  priors for inverse problems in imaging [27] , [28] , [18] , [29] , [30] .  ... 
arXiv:2107.02848v2 fatcat:go27sivhubb7lbki2med32wni4

Unconstrained Monotonic Neural Networks [article]

Antoine Wehenkel, Gilles Louppe
2021 arXiv   pre-print
These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous probability distributions.  ...  We evaluate our new invertible building block within a new autoregressive flow (UMNN-MAF) and demonstrate its effectiveness on density estimation experiments.  ...  Acknowledgments The authors would like to acknowledge Matthia Sabatelli, Nicolas Vecoven, Antonio Sutera and Louis Wehenkel for useful feedback on the manuscript.  ... 
arXiv:1908.05164v3 fatcat:agqhtvuq2bdpbog4g7i75wtc5y
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