arXiv subjects

Kundan Kumar

Publications and source records attributed to Kundan Kumar.

65 records · Page 4Linked to original sources

arXiv2018

Transport of polymer particles in a oil-water flow in porous media: enhancing oil recovery

We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.

physics.flu-dyn↗

arXiv2018

A parallel-in-time fixed-stress splitting method for Biot's consolidation model

In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress splitting method, which has been widely used as solution method of these problems. This new approach forgets about the sequential nature of the temporal variable and considers the time direction as a further direction for parallelization. We present a rigorous convergence analysis of the method and a numerical experiment to demonstrate the robust behaviour of the algorithm.

math.NA↗

arXiv2018

Linear iterative schemes for doubly degenerate parabolic equations

Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation. Here the backward Euler method is combined with a mixed finite element method scheme, which results in a stable and locally mass-conservative scheme. At the same time, at each time step one has to solve a non-linear algebraic system, for which linear iterations are needed. Finding robust and convergent ones is particularly challenging here, since both slow and fast diffusion cases are allowed. Commonly used schemes, like Newton and Picard iterations, are defined either for non-degenerate problems, or after regularising the problem in the case of degenerate ones. Convergence is guaranteed only if the initial guess is sufficiently close to the solution, which translates into severe restrictions on the time step. Here we discuss a linear iterative scheme which builds on the $L$-scheme, and does not employ any regularisation. We prove its rigourous convergence, which is obtained for mild restrictions on the time step. Finally, we give numerical results confirming the theoretical ones, and compare the behaviour of the scheme with other schemes.

math.NA↗

arXiv2017

ObamaNet: Photo-realistic lip-sync from text

We present ObamaNet, the first architecture that generates both audio and synchronized photo-realistic lip-sync videos from any new text. Contrary to other published lip-sync approaches, ours is only composed of fully trainable neural modules and does not rely on any traditional computer graphics methods. More precisely, we use three main modules: a text-to-speech network based on Char2Wav, a time-delayed LSTM to generate mouth-keypoints synced to the audio, and a network based on Pix2Pix to generate the video frames conditioned on the keypoints.

cs.CV↗

arXiv2017

A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media

In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed numerical scheme is based on backward Euler for the temporal discretization and mixed finite element method (MFEM) for the discretization in space. Continuous, semi-discrete (continuous in space) and fully discrete variational formulations are set up and the existence and uniqueness of solutions is discussed. Error estimates are presented to prove the convergence of the scheme. The non-linear systems within each time step are solved by a robust linearization method. This iterative method does not involve any regularization step. The convergence of the linearization scheme is rigorously proved under the assumption of a Lipschitz continuous saturation. The case of a Hölder continuous saturation is also discussed, a rigorous convergence proof being given for Richards' equation. Numerical results are presented to sustain the theoretical findings.

math.NA↗

arXiv2017

SampleRNN: An Unconditional End-to-End Neural Audio Generation Model

In this paper we propose a novel model for unconditional audio generation based on generating one audio sample at a time. We show that our model, which profits from combining memory-less modules, namely autoregressive multilayer perceptrons, and stateful recurrent neural networks in a hierarchical structure is able to capture underlying sources of variations in the temporal sequences over very long time spans, on three datasets of different nature. Human evaluation on the generated samples indicate that our model is preferred over competing models. We also show how each component of the model contributes to the exhibited performance.

cs.SD↗

arXiv2017

Robust iterative schemes for non-linear poromechanics

We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes is shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.

math.NA↗

arXiv2016

On Random Weights for Texture Generation in One Layer Neural Networks

Recent work in the literature has shown experimentally that one can use the lower layers of a trained convolutional neural network (CNN) to model natural textures. More interestingly, it has also been experimentally shown that only one layer with random filters can also model textures although with less variability. In this paper we ask the question as to why one layer CNNs with random filters are so effective in generating textures? We theoretically show that one layer convolutional architectures (without a non-linearity) paired with the an energy function used in previous literature, can in fact preserve and modulate frequency coefficients in a manner so that random weights and pretrained weights will generate the same type of images. Based on the results of this analysis we question whether similar properties hold in the case where one uses one convolution layer with a non-linearity. We show that in the case of ReLu non-linearity there are situations where only one input will give the minimum possible energy whereas in the case of no nonlinearity, there are always infinite solutions that will give the minimum possible energy. Thus we can show that in certain situations adding a ReLu non-linearity generates less variable images.

cs.CV↗

arXiv2016

PixelVAE: A Latent Variable Model for Natural Images

Natural image modeling is a landmark challenge of unsupervised learning. Variational Autoencoders (VAEs) learn a useful latent representation and model global structure well but have difficulty capturing small details. PixelCNN models details very well, but lacks a latent code and is difficult to scale for capturing large structures. We present PixelVAE, a VAE model with an autoregressive decoder based on PixelCNN. Our model requires very few expensive autoregressive layers compared to PixelCNN and learns latent codes that are more compressed than a standard VAE while still capturing most non-trivial structure. Finally, we extend our model to a hierarchy of latent variables at different scales. Our model achieves state-of-the-art performance on binarized MNIST, competitive performance on 64x64 ImageNet, and high-quality samples on the LSUN bedrooms dataset.

cs.LG↗

arXiv2015

Deep Value of Information Estimators for Collaborative Human-Machine Information Gathering

Effective human-machine collaboration can significantly improve many learning and planning strategies for information gathering via fusion of 'hard' and 'soft' data originating from machine and human sensors, respectively. However, gathering the most informative data from human sensors without task overloading remains a critical technical challenge. In this context, Value of Information (VOI) is a crucial decision-theoretic metric for scheduling interaction with human sensors. We present a new Deep Learning based VOI estimation framework that can be used to schedule collaborative human-machine sensing with computationally efficient online inference and minimal policy hand-tuning. Supervised learning is used to train deep convolutional neural networks (CNNs) to extract hierarchical features from 'images' of belief spaces obtained via data fusion. These features can be associated with soft data query choices to reliably compute VOI for human interaction. The CNN framework is described in detail, and a performance comparison to a feature-based POMDP scheduling policy is provided. The practical feasibility of our method is also demonstrated on a mobile robotic search problem with language-based semantic human sensor inputs.

cs.HC↗

arXiv2014

Homogenization of a pore scale model for precipitation and dissolution in porous media

In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a coupled system of evolution equations, involving a parabolic equation and an ordinary differential equation. The former models ion transport and is defined in a periodically perforated medium. It is further coupled through the boundary conditions to the latter, defined on the boundaries of the perforations and modelling the dissolution and precipitation of the precipitate. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but multi-valued mapping. Due to this, the micro-scale solution lacks regularity. With $\ep$ being the scale parameter (the ratio between the micro scale and the macro scale length), we adopt the 2-scale framework to achieve the convergence of the homogenization procedure as $\ep$ approaches zero.

math.AP↗