arXiv subjects

Shantanu Shahane

Publications and source records attributed to Shantanu Shahane.

15 recordsLinked to original sources

arXiv2026

From Lagging to Leading: Validating Hard Braking Events as High-Density Indicators of Segment Crash Risk

Identifying high crash risk road segments and accurately predicting crash incidence is fundamental to implementing effective safety countermeasures. While collision data inherently reflects risk, the infrequency and inconsistent reporting of crashes present a major challenge to robust risk prediction models. The proliferation of connected vehicle technology offers a promising avenue to leverage high-density safety metrics for enhanced crash forecasting. A Hard-Braking Event (HBE), interpreted as an evasive maneuver, functions as a potent proxy for elevated driving risk due to its demonstrable correlation with underlying crash causal factors. Crucially, HBE data is significantly more readily available across the entire road network than conventional collision records. This study systematically evaluated the correlation at individual road segment level between police-reported collisions and aggregated and anonymized HBEs identified via the Google Android Auto platform, utilizing datasets from California and Virginia. Empirical evidence revealed that HBEs occur at a rate magnitudes higher than traffic crashes. Employing the state-of-the-practice Negative-Binomial regression models, the analysis established a statistically significant positive correlation between the HBE rate and the crash rate: road segments exhibiting a higher frequency of HBEs were consistently associated with a greater incidence of crashes. This sophisticated model incorporated and controlled for various confounding factors, including road type, speed profile, proximity to ramps, and road segment slope. The HBEs derived from connected vehicle technology thus provide a scalable, high-density safety surrogate metric for network-wide traffic safety assessment, with the potential to optimize safer routing recommendations and inform the strategic deployment of active safety countermeasures.

cs.OH↗

arXiv2024

Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme

Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness of the solution, dynamically adapting the stencil weights based on local solution features. As rational neural networks can represent fast transitions between smooth and sharp regimes, this approach achieves a granular reconstruction with significantly reduced dissipation, improving the accuracy of the simulation. The network is trained offline on a carefully chosen dataset of analytical functions, bypassing the need for differentiable solvers. We also propose a robust model selection criterion based on estimates of the interpolation's convergence order on a set of test functions, which correlates better with the model performance in downstream tasks. We demonstrate the effectiveness of our approach on several one-, two-, and three-dimensional fluid flow problems: our scheme generalizes across grid resolutions while handling smooth and discontinuous solutions. In most cases, our rational network-based scheme achieves higher accuracy than conventional WENO3 with the same stencil size, and in a few of them, it achieves accuracy comparable to WENO5, which uses a larger stencil.

math.NA↗

arXiv2022

Simulation of Heat Conduction in Complex Domains of Multi-material Composites using a Meshless Method

Several engineering applications involve complex materials with significant and discontinuous variations in thermophysical properties. These include materials for thermal storage, biological tissues with blood capillaries, etc. For such applications, numerical simulations must exercise care in not smearing the interfaces by interpolating variables across the interfaces of the subdomains. In this paper, we describe a high accuracy meshless method that uses domain decomposition and cloud-based interpolation of scattered data to solve the heat conduction equation in such situations. The polyharmonic spline (PHS) function with appended polynomial of prescribed degree is used for discretization. A flux balance condition is satisfied at the interface points and the clouds of interpolation points are restricted to be within respective domains. Compared with previously proposed meshless algorithms with domain decomposition, the cloud-based interpolations are numerically better conditioned, and achieve high accuracy through the appended polynomial. The accuracy of the algorithm is demonstrated in several two and three dimensional problems using manufactured solutions to the heat conduction equation with sharp discontinuity in thermal conductivity. Subsequently, we demonstrate the applicability of the algorithm to solve heat conduction in complex domains with practical boundary conditions and internal heat generation. Systematic computations with varying conductivity ratios, interpoint spacing and degree of appended polynomial are performed to investigate the accuracy of the algorithm.

math.NA↗

arXiv2022

Surrogate Neural Network Model for Sensitivity Analysis and Uncertainty Quantification of the Mechanical Behavior in the Optical Lens-Barrel Assembly

Surrogate neural network-based models have been lately trained and used in a variety of science and engineering applications where the number of evaluations of a target function is limited by execution time. In cell phone camera systems, various errors, such as interferences at the lens-barrel and lens-lens interfaces and axial, radial, and tilt misalignments, accumulate and alter profile of the lenses in a stochastic manner which ultimately changes optical focusing properties. Nonlinear finite element analysis of the stochastic mechanical behavior of lenses due to the interference fits is used on high-performance computing (HPC) to generate sufficient training and testing data for subsequent deep learning. Once properly trained and validated, the surrogate neural network model enabled accurate and almost instant evaluations of millions of function evaluations providing the final lens profiles. This computational model, enhanced by artificial intelligence, enabled us to efficiently perform Monte-Carlo analysis for sensitivity and uncertainty quantification of the final lens profile to various interferences. It can be further coupled with an optical analysis to perform ray tracing and analyze the focal properties of the lens module. Moreover, it can provide a valuable tool for optimizing tolerance design and intelligent components matching for many similar press-fit assembly processes.

cs.CE↗

arXiv2022

Consistency and Convergence of a High Order Accurate Meshless Method for Solution of Incompressible Fluid Flows

Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of coefficients. When a non-conservative discretization method such as finite difference, finite element, or spectral scheme is used, such a matrix also generates an inconsistency which makes the residuals in the iterative solution to saturate at a threshold level that depends on the spatial resolution and order of the discretization scheme. In this paper, we examine inconsistency for a high-order meshless discretization scheme suitable for solving the equations on a complex domain. The high order meshless method uses polyharmonic spline radial basis functions (PHS-RBF) with appended polynomials to interpolate scattered data and constructs the discrete equations by collocation. The PHS-RBF provides the flexibility to vary the order of discretization by increasing the degree of the appended polynomial. In this study, we examine the convergence of the inconsistency for different spatial resolutions and for different degrees of the appended polynomials by solving the Poisson equation for a manufactured solution as well as the Navier-Stokes equations for several fluid flows. We observe that the inconsistency decreases faster than the error in the final solution, and eventually becomes vanishing small at sufficient spatial resolution. The rate of convergence of the inconsistency is observed to be similar or better than the rate of convergence of the discretization errors. This beneficial observation makes it unnecessary to regularize the Poisson equation by fixing either the mean pressure or pressure at an arbitrary point. A simple point solver such as the SOR is seen to be well-convergent, although it can be further accelerated using multilevel methods.

math.NA↗

arXiv2022

Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. Two-dimensional time-dependent Navier Stokes equations are solved using a meshless method where interpolations are done with Polyharmonic Spline Radial Basis Functions. The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 and 2000. Formation of Moffatt like vortices in the wide-gap region of the model is observed and some benchmark data are provided for various cases that are simulated.

physics.flu-dyn↗

arXiv2021

Sensitivity Analysis of Lift and Drag Coefficients for Flow over Elliptical Cylinders of Arbitrary Aspect Ratio and Angle of Attack using Neural Network

Flow over bluff bodies has multiple engineering applications and thus, has been studied for decades. The lift and drag coefficients are practically important in the design of many components such as automobiles, aircrafts, buildings etc. These coefficients vary significantly with Reynolds number and geometric parameters of the bluff body. In this study, we have analyzed the sensitivity of lift and drag coefficients on single and tandem elliptic cylinders to cylinder aspect ratios, angles of attack, cylinder separation, and flow Reynolds number. Sensitivity analysis with Monte-Carlo algorithm requires several function evaluations, which is infeasible with high-fidelity computational simulations. We have therefore trained multilayer perceptron neural networks (MLPNN) using computational fluid dynamics data to estimate the lift and drag coefficients efficiently. Line plots of the variations in lift and drag as functions of the governing parameters are also presented. The present approach is applicable to study of various other bluff body configurations.

physics.flu-dyn↗

arXiv2021

A High-Order Accurate Meshless Method for Solution of Incompressible Fluid Flow Problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or elements, issues such as grid skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse Multiquadrics are some of the most popular RBFs used for the solutions of fluid flow and heat transfer problems. But they have additional shape parameters that have to be fine tuned for accuracy and stability. Moreover, they also face stagnation error when the point density is increased for accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials. In this research, we extend the PHS-RBF method for the solution of incompressible Navier-Stokes equations. A fractional step method with explicit convection and explicit diffusion terms is combined with a pressure Poisson equation to satisfy the momentum and continuity equations. Systematic convergence tests have been performed for five model problems with two of them having analytical solutions. We demonstrate fast convergence both with refinement of number of points and degree of appended polynomials. The method is further applied to solve problems such as lid-driven cavity and vortex shedding over circular cylinder. We have also analyzed the performance of this approach for solution of Euler equations. The proposed method shows promise to solve fluid flow and heat transfer problems in complex domains with high accuracy.

math.NA↗

arXiv2021

Application of a High Order Accurate Meshless Method to Solution of Heat Conduction in Complex Geometries

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial basis functions (RBFs) have been popularly used as high accuracy interpolants of function values at scattered locations. In this paper, we apply the polyharmonic splines (PHS) as the RBF together with appended polynomial and solve the heat conduction equation in several geometries using a collocation procedure. We demonstrate the expected exponential convergence of the numerical solution as the degree of the appended polynomial is increased. The method holds promise to solve several different governing equations in thermal sciences.

math.NA↗

arXiv2021

A Semi-Implicit Meshless Method for Incompressible Flows in Complex Geometries

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as interpolants. Higher-order polynomials are appended to polyharmonic splines (PHS-RBF) and a collocation method is used to derive the interpolation coefficients. The interpolating kernels are then differentiated and the partial-differential equations are satisfied by collocation at the scattered points. The PHS-RBF interpolation is shown to be exponentially convergent with discretization errors decreasing as a high power of a representative distance between points. We present here a semi-implicit algorithm for time-dependent and steady state fluid flows in complex domains. At each time step, several iterations are performed to converge the momentum and continuity equations. A Poisson equation for pressure corrections is formulated by imposing divergence free condition on the iterated velocity field. At each time step, the momentum and pressure correction equations are repeatedly solved until the velocities and pressure converge to a pre-specified tolerance. We have demonstrated the convergence and discretization accuracy of the algorithm for two model problems and simulated three other complex problems. In all cases, the algorithm is stable for Courant numbers in excess of ten. The algorithm has the potential to accurately and efficiently solve many fluid flow and heat transfer problems in complex domains. An open source code Meshless Multi-Physics Software (MeMPhyS) is available for interested users of the algorithm.

math.NA↗

arXiv2021

A Non-Nested Multilevel Method for Meshless Solution of the Poisson Equation in Heat Transfer and Fluid Flow

We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve exponential convergence of discretization errors. The interpolations are performed over local clouds of points and the Poisson equation is collocated at each of the scattered points, resulting in a sparse set of discrete equations for the unkown variables. To solve this set of equations, we have developed a non-nested multilevel algorithm utilizing multiple independently generated coarse sets of points. The restriction and prolongation operators are also constructed with the same RBF interpolations procedure. The performance of the algorithm for Dirichlet and all-Neumann boundary conditions is evaluated in three model geometries using a manufactured solution. For Dirichlet boundary conditions, rapid convergence is observed using SOR point solver as the relaxation scheme. For cases of all-Neumann boundary conditions, convergence is seen to slow down with the degree of the appended polynomial. However, when the multilevel procedure is combined with a GMRES algorithm, the convergence is seen to significantly improve. The GMRES accelerated multilevel algorithm is included in a fractional step method to solve incompressible Navier-Stokes equations.

math.NA↗

arXiv2021

Numerical Simulations of Frost Growth Using Mixture Model on Surfaces with Different Wettability

Frost growth on cold surfaces is a transient process with coupled heat and mass transfer. Due to multiple factors such as humidity, temperature, flow velocity and constantly changing thermal properties as frost grows, precise prediction can be challenging. Especially when the geometry of the frosting surfaces gets complicated, it requires a balance of computing accuracy and efficiency. In this work, a numerical model is developed to predict frost growth considering the effect of the above parameters. Mixture model is adapted to improve the computational efficiency and the unstructured grids add the flexibility to extend the model to complex geometries. The predicted frost growth rate matches well with the experimental data reported in the literature under similar conditions. The model predicts reasonable growth trend of frost as the surface temperature, air temperature, humidity and flow velocity vary. The surface wettability effect is well captured at the early stage of frosting and it shows a higher frost growth rate on surfaces with a higher wettability.

physics.flu-dyn↗

arXiv2020

Optimization of Solidification in Die Casting using Numerical Simulations and Machine Learning

In this paper, we demonstrate the combination of machine learning and three dimensional numerical simulations for multi-objective optimization of low pressure die casting. The cooling of molten metal inside the mold is achieved typically by passing water through the cooling lines in the die. Depending on the cooling line location, coolant flow rate and die geometry, nonuniform temperatures are imposed on the molten metal at the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. A finite volume based numerical solver is used to determine the temperature-time history and correlate the inputs to outputs. The objective of this research is to develop and demonstrate a procedure to obtain the initial and wall temperatures so as to optimize the product quality. The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization in this work. The number of function evaluations required for NSGA-II can be of the order of millions and hence, the finite volume solver cannot be used directly for optimization. Therefore, a multilayer perceptron feed-forward neural network is first trained using the results from the numerical solution of the fluid flow and energy equations and is subsequently used as a surrogate model. As an assessment, simplified versions of the actual problem are designed to first verify results of the genetic algorithm. An innovative local sensitivity based approach is then used to rank the final Pareto optimal solutions and select a single best design.

cs.CE↗

arXiv2018

Uncertainty Quantification in Three Dimensional Natural Convection using Polynomial Chaos Expansion and Deep Neural Networks

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation and global sensitivity analysis. In case A, stochastic variation is introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers) with an assumption that the boundary temperature is uniform. Being a two dimensional stochastic problem, the polynomial chaos expansion (PCE) method is used as a surrogate model. Case B deals with non-uniform stochasticity in the boundary temperature. Instead of the traditional Gaussian process model with the Karhunen-Lo$\grave{e}$ve expansion, a novel approach is successfully implemented to model uncertainty in the boundary condition. The boundary is divided into multiple domains and the temperature imposed on each domain is assumed to be an independent and identically distributed (i.i.d) random variable. Deep neural networks are trained with the boundary temperatures as inputs and Nusselt number, internal temperature or velocities as outputs. The number of domains which is essentially the stochastic dimension is 4, 8, 16 or 32. Rigorous training and testing process shows that the neural network is able to approximate the outputs to a reasonable accuracy. For a high stochastic dimension such as 32, it is computationally expensive to fit the PCE. This paper demonstrates a novel way of using the deep neural network as a surrogate modeling method for uncertainty quantification with the number of simulations much fewer than that required for fitting the PCE, thus, saving the computational cost.

math.NA↗

arXiv2018

Finite Volume Simulation Framework for Die Casting with Uncertainty Quantification

The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters. Rigorous validation is presented using published experimental results of a solidification problem.

math.NA↗