arXiv subjects

Kumar Saurabh

Publications and source records attributed to Kumar Saurabh.

At least 19 recordsLinked to original sources

arXiv2026

Field conserving adaptive mesh refinement (AMR) scheme on massively parallel adaptive octree meshes

Adaptive mesh refinement (AMR) is widely used to efficiently resolve localized features in time-dependent partial differential equations (PDEs) by selectively refining and coarsening the mesh. However, in long-horizon simulations, repeated intergrid interpolations can introduce systematic drift in conserved quantities, especially for variational discretizations with continuous basis functions. While interpolation from parent-to-child during refinement in continuous Galerkin (CG) discretizations is naturally conservative, the standard injection-based child-to-parent coarsening interpolation is generally not. We propose a simple, scalable field-conserving coarsening operator for parallel, octree-based AMR. The method enforces discrete global conservation during coarsening by first computing field conserving coarse-element values at quadrature points and then recovering coarse nodal degrees of freedom via an $L^2$ projection (mass-matrix solve), which simultaneously controls the $L_2$ error. We evaluate the approach on mass-conserving phase-field models, including the Cahn--Hilliard and Cahn--Hilliard--Navier--Stokes systems, and compare against injection in terms of conservation error, solution quality, and computational cost.

math.NA↗

arXiv2024

Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples

We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the ``full" space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach.

math.NA↗

arXiv2023

TMAP: A Threat Modeling and Attack Path Analysis Framework for Industrial IoT Systems (A Case Study of IoM and IoP)

Industrial cyber-physical systems (ICPS) are gradually integrating information technology and automating industrial processes, leading systems to become more vulnerable to malicious actors. Thus, to deploy secure Industrial Control and Production Systems (ICPS) in smart factories, cyber threats and risks must be addressed. To identify all possible threats, Threat Modeling is a promising solution. Despite the existence of numerous methodological solutions for threat modeling in cyber-physical systems (CPS), current approaches are ad hoc and inefficient in providing clear insights to researchers and organizations involved in IIoT technologies. These approaches lack a comprehensive analysis of cyber threats and fail to facilitate effective path analysis across the ICPS lifecycle, incorporating smart manufacturing technologies and tools. To address these gaps, a novel quantitative threat modeling approach is proposed, aiming to identify probable attack vectors, assess the path of attacks, and evaluate the magnitude of each vector. This paper also explains the execution of the proposed approach with two case studies, namely the industrial manufacturing line, i.e., the Internet of Manufacturing (IoM), and the power and industry, i.e., the Internet of Production (IoP).

cs.CR↗

arXiv2023

Optimal Surrogate Boundary Selection and Scalability Studies for the Shifted Boundary Method on Octree Meshes

The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed boundary methods (IBMs) alleviate the usually laborious and time-consuming process of creating body-fitted meshes around complex geometry models (described by CAD or other representations, e.g., STL, point clouds), especially when high levels of mesh adaptivity are required. In this work, we advance the field of IBM in the context of the recently developed Shifted Boundary Method (SBM). In the SBM, the location where boundary conditions are enforced is shifted from the actual boundary of the immersed object to a nearby surrogate boundary, and boundary conditions are corrected utilizing Taylor expansions. This approach allows choosing surrogate boundaries that conform to a Cartesian mesh without losing accuracy or stability. Our contributions in this work are as follows: (a) we show that the SBM numerical error can be greatly reduced by an optimal choice of the surrogate boundary, (b) we mathematically prove the optimal convergence of the SBM for this optimal choice of the surrogate boundary, (c) we deploy the SBM on massively parallel octree meshes, including algorithmic advances to handle incomplete octrees, and (d) we showcase the applicability of these approaches with a wide variety of simulations involving complex shapes, sharp corners, and different topologies. Specific emphasis is given to Poisson's equation and the linear elasticity equations.

math.NA↗

arXiv2023

Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization

We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with adaptive space-time mesh refinement provide efficient and accurate solutions. The accuracy of the space-time solutions is illustrated against analytical solutions as well as against numerical solutions using a conventional time-marching algorithm.

math.NA↗

arXiv2023

High-Resolution Thermal Simulation Framework for Extrusion-based Additive Manufacturing of Complex Geometries

Accurate simulation of the printing process is essential for improving print quality, reducing waste, and optimizing the printing parameters of extrusion-based additive manufacturing. Traditional additive manufacturing simulations are very compute-intensive and are not scalable to simulate even moderately sized geometries. In this paper, we propose a general framework for creating a digital twin of the dynamic printing process by performing physics simulations with the intermediate print geometries. Our framework takes a general extrusion-based additive manufacturing G-code, generates an analysis-suitable voxelized geometry representation from the print schedule, and performs physics-based (transient thermal) simulations of the printing process. Our approach leverages adaptive octree meshes for both geometry representation as well as for fast simulations to address real-time predictions. We demonstrate the effectiveness of our method by simulating the printing of complex geometries at high voxel resolutions with both sparse and dense infills. Our results show that this approach scales to high voxel resolutions and can predict the transient heat distribution as the print progresses. Because the simulation runs faster than real print time, the same engine could, in principle, feed thermal predictions back to the machine controller (e.g., to adjust fan speed or extrusion rate). The present study establishes the computational foundations for a real-time digital twin, which can be used for closed control loop control in the future.

cs.GR↗

arXiv2023

Direct numerical simulation of electrokinetic transport phenomena in fluids: variational multi-scale stabilization and octree-based mesh refinement

Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the diffuse charge layer (DCL), (b) stiff coupling due to fast charge relaxation times, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices. In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective flows often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows the use of tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the DCL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples.

math.NA↗

arXiv2022

SciAI4Industry -- Solving PDEs for industry-scale problems with deep learning

Solving partial differential equations with deep learning makes it possible to reduce simulation times by multiple orders of magnitude and unlock scientific methods that typically rely on large numbers of sequential simulations, such as optimization and uncertainty quantification. Two of the largest challenges of adopting scientific AI for industrial problem settings is that training datasets must be simulated in advance and that neural networks for solving large-scale PDEs exceed the memory capabilities of current GPUs. We introduce a distributed programming API in the Julia language for simulating training data in parallel on the cloud and without requiring users to manage the underlying HPC infrastructure. In addition, we show that model-parallel deep learning based on domain decomposition allows us to scale neural networks for solving PDEs to commercial-scale problem settings and achieve above 90% parallel efficiency. Combining our cloud API for training data generation and model-parallel deep learning, we train large-scale neural networks for solving the 3D Navier-Stokes equation and simulating 3D CO2 flow in porous media. For the CO2 example, we simulate a training dataset based on a commercial carbon capture and storage (CCS) project and train a neural network for CO2 flow simulation on a 3D grid with over 2 million cells that is 5 orders of magnitudes faster than a conventional numerical simulator and 3,200 times cheaper.

cs.DC↗

arXiv2022

Neural PDE Solvers for Irregular Domains

Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically address the imposition of Dirichlet/Neumann boundary conditions over irregular domain boundaries. In this paper, we present a framework to neurally solve partial differential equations over domains with irregularly shaped (non-rectilinear) geometric boundaries. Our network takes in the shape of the domain as an input (represented using an unstructured point cloud, or any other parametric representation such as Non-Uniform Rational B-Splines) and is able to generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a novel approach for identifying the interior and exterior of the computational grid in a differentiable manner. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase a wide variety of applications, along with favorable comparisons with ground truth solutions.

cs.LG↗

arXiv2022

CyRSoXS: A GPU-accelerated virtual instrument for Polarized Resonant Soft X-ray Scattering (P-RSoXS)

Polarized Resonant Soft X-ray scattering (P-RSoXS) has emerged as a powerful synchrotron-based tool that combines principles of X-ray scattering and X-ray spectroscopy. P-RSoXS provides unique sensitivity to molecular orientation and chemical heterogeneity in soft materials such as polymers and biomaterials. Quantitative extraction of orientation information from P-RSoXS pattern data is challenging because the scattering processes originate from sample properties that must be represented as energy-dependent three-dimensional tensors with heterogeneities at nanometer to sub-nanometer length scales. We overcome this challenge by developing an open-source virtual instrument that uses GPUs to simulate P-RSoXS patterns from real-space material representations with nanoscale resolution. Our computational framework CyRSoXS (https://github.com/usnistgov/cyrsoxs) is designed to maximize GPU performance. We demonstrate the accuracy and robustness of our approach by validating against an extensive set of test cases, which include both analytical solutions and numerical comparisons, demonstrating a speedup of over three orders relative to the current state-of-the-art simulation software. Such fast simulations open up a variety of applications that were previously computationally infeasible, including (a) pattern fitting, (b) co-simulation with the physical instrument for operando analytics, data exploration, and decision support, (c) data creation and integration into machine learning workflows, and (d) utilization in multi-modal data assimilation approaches. Finally, we abstract away the complexity of the computational framework from the end-user by exposing CyRSoXS to Python using Pybind. This eliminates I/O requirements for large-scale parameter exploration and inverse design, and democratizes usage by enabling seamless integration with a Python ecosystem (https://github.com/usnistgov/nrss).

physics.comp-ph↗

arXiv2022

Breakup dynamics in primary jet atomization using mesh- and interface- refined Cahn-Hilliard Navier-Stokes

We present a technique to perform interface-resolved simulations of complex breakup dynamics in two-phase flows using the Cahn-Hilliard Navier-Stokes equations. The method dynamically decreases the interface thickness parameter in relevant regions and simultaneously increases local mesh resolution, preventing numerical artifacts. We perform a detailed numerical simulation of pulsed jet atomization that shows a complex cascade of break-up mechanisms involving sheet rupture and filament formation. To understand the effect of refinement on the breakup, we analyze the droplet size distribution. The proposed approach opens up resolved simulations for various multiphase flow phenomena.

physics.flu-dyn↗

arXiv2022

Scalable adaptive algorithms for next-generation multiphase flow simulations

High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the fluid-fluid interfaces. However, the increased resolution comes at a higher computational cost. In this work, we propose algorithmic advances that aim to reduce the computational cost without compromising on the physics by selectively detecting key regions of interest (droplets/filaments) that require significantly higher resolution. The framework uses an adaptive octree-based meshing framework that is integrated with PETSc's linear algebra solvers. We demonstrate scaling of the framework up to 114,688 processes on TACC's Frontera. Finally, we deploy the framework to simulate one of the most resolved simulations of primary jet atomization. This simulation -- equivalent to 35 trillion grid points on a uniform grid -- is 64 times larger than the current state-of-the-art simulations and provides unprecedented insights into an important flow physics problem with a diverse array of engineering applications.

physics.comp-ph↗

arXiv2022

NFDLM: A Lightweight Network Flow based Deep Learning Model for DDoS Attack Detection in IoT Domains

In the recent years, Distributed Denial of Service (DDoS) attacks on Internet of Things (IoT) devices have become one of the prime concerns to Internet users around the world. One of the sources of the attacks on IoT ecosystems are botnets. Intruders force IoT devices to become unavailable for its legitimate users by sending large number of messages within a short interval. This study proposes NFDLM, a lightweight and optimised Artificial Neural Network (ANN) based Distributed Denial of Services (DDoS) attack detection framework with mutual correlation as feature selection method which produces a superior result when compared with Long Short Term Memory (LSTM) and simple ANN. Overall, the detection performance achieves approximately 99\% accuracy for the detection of attacks from botnets. In this work, we have designed and compared four different models where two are based on ANN and the other two are based on LSTM to detect the attack types of DDoS.

cs.CR↗

arXiv2022

LBDMIDS: LSTM Based Deep Learning Model for Intrusion Detection Systems for IoT Networks

In the recent years, we have witnessed a huge growth in the number of Internet of Things (IoT) and edge devices being used in our everyday activities. This demands the security of these devices from cyber attacks to be improved to protect its users. For years, Machine Learning (ML) techniques have been used to develop Network Intrusion Detection Systems (NIDS) with the aim of increasing their reliability/robustness. Among the earlier ML techniques DT performed well. In the recent years, Deep Learning (DL) techniques have been used in an attempt to build more reliable systems. In this paper, a Deep Learning enabled Long Short Term Memory (LSTM) Autoencoder and a 13-feature Deep Neural Network (DNN) models were developed which performed a lot better in terms of accuracy on UNSW-NB15 and Bot-IoT datsets. Hence we proposed LBDMIDS, where we developed NIDS models based on variants of LSTMs namely, stacked LSTM and bidirectional LSTM and validated their performance on the UNSW\_NB15 and BoT\-IoT datasets. This paper concludes that these variants in LBDMIDS outperform classic ML techniques and perform similarly to the DNN models that have been suggested in the past.

cs.CR↗

arXiv2022

Terrain Classification using Transfer Learning on Hyperspectral Images: A Comparative study

A Hyperspectral image contains much more number of channels as compared to a RGB image, hence containing more information about entities within the image. The convolutional neural network (CNN) and the Multi-Layer Perceptron (MLP) have been proven to be an effective method of image classification. However, they suffer from the issues of long training time and requirement of large amounts of the labeled data, to achieve the expected outcome. These issues become more complex while dealing with hyperspectral images. To decrease the training time and reduce the dependence on large labeled dataset, we propose using the method of transfer learning. The hyperspectral dataset is preprocessed to a lower dimension using PCA, then deep learning models are applied to it for the purpose of classification. The features learned by this model are then used by the transfer learning model to solve a new classification problem on an unseen dataset. A detailed comparison of CNN and multiple MLP architectural models is performed, to determine an optimum architecture that suits best the objective. The results show that the scaling of layers not always leads to increase in accuracy but often leads to overfitting, and also an increase in the training time.The training time is reduced to greater extent by applying the transfer learning approach rather than just approaching the problem by directly training a new model on large datasets, without much affecting the accuracy.

cs.CV↗

arXiv2021

Case study of SARS-CoV-2 transmission risk assessment in indoor environments using cloud computing resources

Complex flow simulations are conventionally performed on HPC clusters. However, the limited availability of HPC resources and steep learning curve of executing on traditional supercomputer infrastructure has drawn attention towards deploying flow simulation software on the cloud. We showcase how a complex computational framework -- that can evaluate COVID-19 transmission risk in various indoor classroom scenarios -- can be abstracted and deployed on cloud services. The availability of such cloud-based personalized planning tools can enable educational institutions, medical institutions, public sector workers (courthouses, police stations, airports, etc.), and other entities to comprehensively evaluate various in-person interaction scenarios for transmission risk. We deploy the simulation framework on the Azure cloud framework, utilizing the Dendro-kT mesh generation tool and PETSc solvers. The cloud abstraction is provided by RocketML cloud infrastructure. We compare the performance of the cloud machines with state-of-the-art HPC machine TACC Frontera. Our results suggest that cloud-based HPC resources are a viable strategy for a diverse array of end-users to rapidly and efficiently deploy simulation software.

cs.DC↗

arXiv2021

Scalable adaptive PDE solvers in arbitrary domains

Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a `good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an $\textit{incomplete}$ octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on $\textit{incomplete}$ octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers ($\mathcal{O}(1-10^6)$) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.

math.NA↗

arXiv2021

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In this work, we present a semi-implicit, projection-based finite element framework for solving the CHNS system. We use a projection-based semi-implicit time discretization for the Navier-Stokes equation and a fully-implicit time discretization for the Cahn-Hilliard equation. We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation. Pressure is decoupled using a projection step, which results in two linear positive semi-definite systems for velocity and pressure, instead of the saddle point system of a pressure-stabilized method. All the linear systems are solved using an efficient and scalable algebraic multigrid (AMG) method. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. The overall approach allows the use of relatively large time steps with much faster time-to-solve than similar fully-implicit methods. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise and Rayleigh-Taylor instability.

math.NA↗