71 citations · 365 across the 27 of their papers we have counts for
29 papers
A high-order, meshless, Lagrangian--Eulerian RBF-FD method for advection--diffusion--reaction on moving manifolds
Matthew Lowery, Grady B. Wright, Varun Shankar
We present a high-order radial basis function-generated finite difference (RBF-FD) method for partial differential equations on moving manifolds o…
Locally Adaptive and Differentiable Regression
Mingxuan Han, Varun Shankar, Jeff M Phillips +1
Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in…
Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics
Hojin Kim, Varun Shankar, Venkatasubramanian Viswanathan +1
Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable…
Importance of equivariant and invariant symmetries for fluid flow modeling
Varun Shankar, Shivam Barwey, Zico Kolter +2
Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning pr…
Differentiable Turbulence: Closure as a partial differential equation constrained optimization
Varun Shankar, Dibyajyoti Chakraborty, Venkatasubramanian Viswanathan +1
Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage…
Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis
Urban Duh, Varun Shankar, Gregor Kosec
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more spec…
Differentiable physics-enabled closure modeling for Burgers' turbulence
Varun Shankar, Vedant Puri, Ramesh Balakrishnan +2
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the different…
Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations
Ramansh Sharma, Varun Shankar
We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial deriva…
MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces
Grady B. Wright, Andrew M. Jones, Varun Shankar
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The metho…
Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow
Varun Shankar, Gavin D. Portwood, Arvind T. Mohan +6
In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence cl…
Immersed boundary simulations of cell-cell interactions in whole blood
Andrew Kassen, Aaron Barrett, Varun Shankar +1
We present a new method for the geometric reconstruction of elastic surfaces simulated by the immersed boundary method with the goal of simulating the motion and interactions of ce…
Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture
M. Keith Ballard, Roman Amici, Varun Shankar +3
We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that generalizes the work of Hansbo and Hansbo to allow multiple Heaviside enrichments with…
A fine-grained parallelization of the immersed boundary method
Andrew Kassen, Varun Shankar, Aaron L Fogelson
We present new algorithms for the parallelization of Eulerian-Lagrangian interaction operations in the immersed boundary method. Our algorithms rely on two well-studied parallel pr…
Pump efficacy in a fluid-structure interaction model of a chain of contracting lymphangions
Hallie Elich, Aaron Barrett, Varun Shankar +1
The transport of lymph through the lymphatic vasculature is the mechanism for returning excess interstitial fluid to the circulatory system, and it is essential for fluid homeostas…
An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains
Varun Shankar, Grady B. Wright, Aaron L. Fogelson
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based…
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds
Varun Shankar, Grady B. Wright, Akil Narayan
We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds…
Asymptotic and numerical analysis of a stochastic PDE model of volume transmission
Sean D. Lawley, Varun Shankar
Volume transmission is an important neural communication pathway in which neurons in one brain region influence the neurotransmitter concentration in the extracellular space of a d…
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces
Varun Shankar, Akil Narayan, Robert M. Kirby
We present a new method for the solution of PDEs on manifolds of co-dimension one using stable scale-free radial basis function (RBF) interpolatio…
Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations
Varun Shankar, Aaron L. Fogelson
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytica…
Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces
Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to novel parameter-free,…
Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing
Vidhi Zala, Varun Shankar, Shankar P. Sastry +1
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or…
Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions
Varun Shankar, Grady Wright
We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are…
The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method: A Generalization of RBF-FD
Varun Shankar
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap paramete…
A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations
Edward J. Fuselier, Varun Shankar, Grady B. Wright
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of th…