Publications (63)
Fractured Poroelastic Media in the Limit of Vanishing Aperture
Maximilian Hörl, Kundan Kumar, Christian Rohde
We consider a poroelastic medium with a thin heterogeneity, also referred to as a fracture. Fluid flow and mechanical deformation inside both bulk and fracture are governed by the…
Transport of polymer particles in a oil-water flow in porous media: enhancing oil recovery
Max A. Endo Kokubun, Florin A. Radu, Eirik Keilegavlen +2
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 whi…
Splitting method for elliptic equations with line sources
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten +1
In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain when the right-hand side is a (1D) line source .…
Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium
Maarten V. de Hoop, Kundan Kumar
We present a mixed dimensional model for a fractured poro-elasic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic mat…
A fixed-stress type splitting method for nonlinear poroelasticity
Johannes Kraus, Kundan Kumar, Maria Lymbery +1
In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the…
Well-posedness of evolutionary differential variational-hemivariational inequalities and applications to frictional contact mechanics
Nadia Skoglund Taki, Kundan Kumar
In this paper, we study the well-posedness of a class of evolutionary variational-hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spa…
Upscaling of unsaturated flow in fractured porous media
Florian List, Kundan Kumar, Iuliu Sorin Pop +1
In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the fl…
Tracking an Underwater Target with Unknown Measurement Noise Statistics Using Variational Bayesian Filters
Shreya Das, Kundan Kumar, Shovan Bhaumik
This paper considers a bearings-only tracking problem using noisy measurements of unknown noise statistics from a passive sensor. It is assumed that the process and measurement noi…
Automated retinal vessel segmentation based on morphological preprocessing and 2D-Gabor wavelets
Kundan Kumar, Debashisa Samal, Suraj
Automated segmentation of vascular map in retinal images endeavors a potential benefit in diagnostic procedure of different ocular diseases. In this paper, we suggest a new unsuper…
A parallel-in-time fixed-stress splitting method for Biot's consolidation model
Manuel Borregales, Kundan Kumar, Florin Adrian Radu +2
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 par…
Numerical analysis of the Biot equations coupled to frictional contact mechanics
Marius Nevland, Kundan Kumar, Inga Berre +2
We consider a mathematical model of a poro-visco-elastic medium subject to frictional contact with a rigid obstacle, and study its numerical approximation. This model couples the B…
On the optimization of the fixed-stress splitting for Biot's equations
Erlend Storvik, Jakub Wiktor Both, Kundan Kumar +2
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular metho…
Numerical simulation of biofilm formation in a microchannel
David Landa-Marbán, Iuliu S. Pop, Kundan Kumar +1
The focus of this paper is the numerical solution of a pore-scale model for the growth of a permeable biofilm. The model includes water flux inside the biofilm, different biofilm c…
A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media
Florin Adrian Radu, Kundan Kumar, Jan Martin Nordbotten +1
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 degenerat…
A Singularity Removal Method for Coupled 1D-3D Flow Models
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten
In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modell…
An upscaled model for permeable biofilm in a thin channel and tube
David Landa-Marbán, Gunhild Bødtker, Kundan Kumar +2
In this paper, we derive upscaled equations for modelling biofilm growth in porous media. The resulting macro-scale mathematical models consider permeable multi-species biofilm inc…
An efficient preconditioner for mixed-dimensional contact poromechanics based on the fixed stress splitting scheme
Yury Zabegaev, Inga Berre, Eirik Keilegavlen +1
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage.…
Blood Vessel Detection using Modified Multiscale MF-FDOG Filters for Diabetic Retinopathy
Debojyoti Mallick, Kundan Kumar, Sumanshu Agarwal
Blindness in diabetic patients caused by retinopathy (characterized by an increase in the diameter and new branches of the blood vessels inside the retina) is a grave concern. Many…
PixelVAE: A Latent Variable Model for Natural Images
Ishaan Gulrajani, Kundan Kumar, Faruk Ahmed +4
Natural image modeling is a landmark challenge of unsupervised learning. Variational Autoencoders (VAEs) learn a useful latent representation and model global structure well but ha…
Communication-Efficient Distributed Kalman Filtering using ADMM
Muhammad Iqbal, Kundan Kumar, Simo Särkkä
This paper addresses the problem of optimal linear filtering in a network of local estimators, commonly referred to as distributed Kalman filtering (DKF). The DKF problem is formul…
SampleRNN: An Unconditional End-to-End Neural Audio Generation Model
Soroush Mehri, Kundan Kumar, Ishaan Gulrajani +5
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 memor…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
Kundan Kumar, Svetlana Kyas, Jan Nordbotten +1
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equat…
Antimony Chalcogenide-based Solid State Sensitizers for Solar Cells: A Forgotten Hero or Low Potential Candidate
Sumanshu Agarwal, Harekrishna Yadav, Kundan Kumar
The use of stibnite (Sb2S3) as sensitizers in the solid-state sensitized solar cells received considerable research interest during the transition of the millennium. However, the u…
A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments
David Landa-Marbán, Na Liu, Iuliu Sorin Pop +5
In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed t…
A History-dependent Dynamic Biot Model
Jakob S. Stokke, Morten Jakobsen, Kundan Kumar +1
In this work, we consider a fully dynamic Biot model that includes memory effects due to evolving permeability. Time integrals are used to account for the change in structure. We p…
The gradient flow structures of thermo-poro-visco-elastic processes in porous media
Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten +1
In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framewor…
Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten +1
In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equ…
Wav2CLIP: Learning Robust Audio Representations From CLIP
Ho-Hsiang Wu, Prem Seetharaman, Kundan Kumar +1
We propose Wav2CLIP, a robust audio representation learning method by distilling from Contrastive Language-Image Pre-training (CLIP). We systematically evaluate Wav2CLIP on a varie…
Radially excited (n=3)charm mesons in heavy quark effective theory
Ritu Garg, Kundan Kumar, Alka Upadhyay
By exploring heavy quark effective theory (HQET), we use theoretical available data for bottom mesons to analysis the masses and decays for n = 3 charm mesons. From the predicted m…
Statistical Linear Regression Approach to Kalman Filtering and Smoothing under Cyber-Attacks
Kundan Kumar, Muhammad Iqbal, Simo Särkkä
Remote state estimation in cyber-physical systems is often vulnerable to cyber-attacks due to wireless connections between sensors and computing units. In such scenarios, adversari…
Fixed stress splitting approach for contact problems in a porous medium
Tameem Almani, Kundan Kumar
We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variati…
Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media
Paulo Lee Kung Caetano Chang, Kundan Kumar
Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO2 sequestration, and ground…
Chunked Autoregressive GAN for Conditional Waveform Synthesis
Max Morrison, Rithesh Kumar, Kundan Kumar +3
Conditional waveform synthesis models learn a distribution of audio waveforms given conditioning such as text, mel-spectrograms, or MIDI. These systems employ deep generative model…
Nonlinear State Estimation using Gaussian Integral
Kundan Kumar, Shovan Bhaumik
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior pr…
Convergent adaptive iterative schemes for solving multi-physics problems
Jakob S. Stokke, Kundan Kumar, Florin A. Radu
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, gi…
Homogenization of a pore scale model for precipitation and dissolution in porous media
Kundan Kumar, Maria Neuss-Radu, Iuliu Sorin Pop
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…
Gaussian Integral based Bayesian Smoother
Rohit Kumar Singh, Kundan Kumar, Shovan Bhaumik
This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant a…
Numerical studies of long-term wettability alteration effects in CO storage applications
David Landa-Marbán, Kundan Kumar, Sarah Eileen Gasda +2
The wettability of the rock surface in porous media has an effect on the constitutive saturation functions that govern capillary pressure and relative permeability. The term wettab…
Robust iterative schemes for non-linear poromechanics
Manuel Borregales, Florin A. Radu, Kundan Kumar +1
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 di…
MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis
Kundan Kumar, Rithesh Kumar, Thibault de Boissiere +6
Previous works (Donahue et al., 2018a; Engel et al., 2019a) have found that generating coherent raw audio waveforms with GANs is challenging. In this paper, we show that it is poss…
Mathematical Modeling, Laboratory Experiments, and Sensitivity Analysis of Bioplug Technology at Darcy Scale
David Landa-Marbán, Gunhild Bødtker, Bartek Florczyk Vik +4
In this paper we study a Darcy-scale mathematical model for biofilm formation in porous media. The pores in the core are divided into three phases: water, oil, and biofilm. The wat…
Iterative solvers for Biot model under small and large deformation
Manuel Antonio Borregales, Kundan Kumar, Jan Martin Nordbotten +1
We consider L-scheme and Newton based solvers for Biot model under small or large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthe…
Application of Top-hat Transformation for Enhanced Blood Vessel Extraction
Tithi Parna Das, Sheetal Praharaj, Sarita Swain +2
In the medical domain, different computer-aided diagnosis systems have been proposed to extract blood vessels from retinal fundus images for the clinical treatment of vascular dise…
Parareal algorithm for coupled elliptic-parabolic problems
Iñigo Jimenez-Ciga, Francisco Gaspar, Kundan Kumar +1
We present a convergence analysis of the parallel-in-time integration method known as the Parareal algorithm for degenerate differential-algebraic systems arising from quasi-static…
Pattern Based Multivariable Regression using Deep Learning (PBMR-DP)
Jiztom Kavalakkatt Francis, Chandan Kumar, Jansel Herrera-Gerena +2
We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensor…
A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements
Kundan Kumar, Shreya Das, Simo Särkkä
This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagran…
Data-driven stress problem under purely normal homogeneous Neumann boundary conditions
Cristian G. Gebhardt, Kundan Kumar, Florin A. Radu
Data-Driven Continuum Mechanics -- the continuous counterpart of Data-Driven Computational Mechanics -- is a modern paradigm that enhances classical continuum mechanics by incorpor…
Linear iterative schemes for doubly degenerate parabolic equations
Jakub W. Both, Kundan Kumar, Jan M. Nordbotten +2
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore low…
Field-scale impacts of long-term wettability alteration in geological CO storage
Abay Kassa, Sarah Eileen Gasda, David Landa-Marbán +2
Constitutive functions that govern macroscale capillary pressure and relative permeability are central in constraining both storage efficiency and sealing properties of CO stor…
Practical approaches to study microbially induced calcite precipitation at the field scale
David Landa-Marbán, Svenn Tveit, Kundan Kumar +1
Microbially induced calcite precipitation (MICP) is a new and sustainable technology which utilizes biochemical processes to create barriers by calcium carbonate cementation; there…
Large-Scale Neuromorphic Spiking Array Processors: A quest to mimic the brain
Chetan Singh Thakur, Jamal Molin, Gert Cauwenberghs +12
Neuromorphic engineering (NE) encompasses a diverse range of approaches to information processing that are inspired by neurobiological systems, and this feature distinguishes neuro…
Parametric Scaling of Preprocessing assisted U-net Architecture for Improvised Retinal Vessel Segmentation
Kundan Kumar, Sumanshu Agarwal
Extracting blood vessels from retinal fundus images plays a decisive role in diagnosing the progression in pertinent diseases. In medical image analysis, vessel extraction is a sem…
A pore-scale study of transport of inertial particles by water in porous media
Max A. Endo Kokubun, Adrian Muntean, Florin A. Radu +4
We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging.…
Implicit linearization method for non-standard two-phase flow in porous media
Abay M. Kassa, Kundan Kumar, Sarah E. Gasda +1
In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function…
NU-GAN: High resolution neural upsampling with GAN
Rithesh Kumar, Kundan Kumar, Vicki Anand +2
In this paper, we propose NU-GAN, a new method for resampling audio from lower to higher sampling rates (upsampling). Audio upsampling is an important problem since productionizing…
High-Fidelity Audio Compression with Improved RVQGAN
Rithesh Kumar, Prem Seetharaman, Alejandro Luebs +2
Language models have been successfully used to model natural signals, such as images, speech, and music. A key component of these models is a high quality neural compression model…
Numerical studies of CO leakage remediation by micp-based plugging technology
David Landa-Marbán, Kundan Kumar, Svenn Tveit +1
Microbially induced calcite precipitation (MICP) is a technology for sealing leakage paths to ensure the safe storage of CO in geological formations. In this work we introduce…
On Random Weights for Texture Generation in One Layer Neural Networks
Mihir Mongia, Kundan Kumar, Akram Erraqabi +1
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 interesting…
Deep Value of Information Estimators for Collaborative Human-Machine Information Gathering
Kin Gwn Lore, Nicholas Sweet, Kundan Kumar +2
Effective human-machine collaboration can significantly improve many learning and planning strategies for information gathering via fusion of 'hard' and 'soft' data originating fro…
A Mixed Approach to the Poisson Problem with Line Sources
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten
In this work we consider the primal mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is non-standard as the…
ObamaNet: Photo-realistic lip-sync from text
Rithesh Kumar, Jose Sotelo, Kundan Kumar +2
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 appro…
Integrating Lagrangian Neural Networks into the Dyna Framework for Reinforcement Learning
Shreya Das, Kundan Kumar, Muhammad Iqbal +4
Model-based reinforcement learning (MBRL) is sample-efficient but depends on the accuracy of the learned dynamics, which are often modeled using black-box methods that do not adher…
Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: an iterative coupling scheme and well-posedness
Maarten V. de Hoop, Kundan Kumar, Ruichao Ye
We study the solution of the system of equations describing the dynamical evolution of spontaneous ruptures generated in a prestressed elastic-gravitational deforming body and gove…