Varun Shankar

Publication Activity (10 Years)

Years Active: 2012-2024
Publications (10 Years): 40

Top Topics

Radial Basis Function

Top Venues

J. Comput. Phys.

SIAM J. Sci. Comput.

J. Sci. Comput.

Publications

Madison Cooley, Shandian Zhe, Robert M. Kirby, Varun Shankar
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation. CoRR (2024)
Ramansh Sharma, Varun Shankar
Ensemble and Mixture-of-Experts DeepONets For Operator Learning. CoRR (2024)
Matthew Lowery, John Turnage, Zachary Morrow, John D. Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning. CoRR (2024)
Urban Duh, Varun Shankar, Gregor Kosec
Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis. J. Sci. Comput. 100 (2) (2024)
Varun Shankar, Romit Maulik, Venkatasubramanian Viswanathan
Differentiable Turbulence. CoRR (2023)
Varun Shankar, Vedant Puri, Ramesh Balakrishnan, Romit Maulik, Venkatasubramanian Viswanathan
Differentiable physics-enabled closure modeling for Burgers' turbulence. Mach. Learn. Sci. Technol. 4 (1) (2023)
Shivam Barwey, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik
Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning. CoRR (2023)
Urban Duh, Varun Shankar, Gregor Kosec
Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis. CoRR (2023)
Grady B. Wright, Andrew C. Jones, Varun Shankar
MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces. SIAM J. Sci. Comput. 45 (2) (2023)
Shivam Barwey, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik
Multiscale graph neural network autoencoders for interpretable scientific machine learning. J. Comput. Phys. 495 (2023)
Varun Shankar, Shivam Barwey, Zico Kolter, Romit Maulik, Venkatasubramanian Viswanathan
Importance of equivariant and invariant symmetries for fluid flow modeling. CoRR (2023)
Mingxuan Han, Varun Shankar, Jeff M. Phillips, Chenglong Ye
Locally Adaptive and Differentiable Regression. CoRR (2023)
Varun Shankar, Romit Maulik, Venkatasubramanian Viswanathan
Differentiable Turbulence II. CoRR (2023)
Grady B. Wright, Andrew M. Jones, Varun Shankar
MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces. CoRR (2022)
Varun Shankar, Vedant Puri, Ramesh Balakrishnan, Romit Maulik, Venkatasubramanian Viswanathan
Differentiable physics-enabled closure modeling for Burgers' turbulence. CoRR (2022)
Andrew T. Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson
Immersed boundary simulations of cell-cell interactions in whole blood. J. Comput. Phys. 469 (2022)
Ramansh Sharma, Varun Shankar
Accelerated Training of Physics Informed Neural Networks (PINNs) using Meshless Discretizations. CoRR (2022)
Ramansh Sharma, Varun Shankar
Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations. NeurIPS (2022)
Andrew T. Kassen, Varun Shankar, Aaron L. Fogelson
A fine-grained parallelization of the immersed boundary method. Int. J. High Perform. Comput. Appl. 36 (4) (2022)
Andrew Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson
Immersed boundary simulations of cell-cell interactions in whole blood. CoRR (2021)
Varun Shankar, Grady B. Wright, Aaron L. Fogelson
An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains. J. Comput. Phys. 445 (2021)
M. Keith Ballard, Roman Amici, Varun Shankar, Lauren A. Ferguson, Michael Braginsky, Robert M. Kirby
Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture. CoRR (2021)
Varun Shankar, Grady B. Wright, Aaron L. Fogelson
An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains. CoRR (2020)
Sean D. Lawley, Varun Shankar
Asymptotic and Numerical Analysis of a Stochastic PDE Model of Volume Transmission. Multiscale Model. Simul. 18 (2) (2020)
Varun Shankar, Grady B. Wright, Akil Narayan
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. SIAM J. Sci. Comput. 42 (4) (2020)
Andrew Kassen, Varun Shankar, Aaron L. Fogelson
A fine-grained parallelization of the immersed boundary method. CoRR (2020)
Varun Shankar, Grady B. Wright, Akil Narayan
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. CoRR (2019)
Varun Shankar, Grady B. Wright
Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions. J. Comput. Phys. 366 (2018)
Vidhi Zala, Varun Shankar, Shankar Prasad Sastry, Robert M. Kirby
Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing. J. Sci. Comput. 77 (1) (2018)
Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces. CoRR (2018)
Varun Shankar, Grady B. Wright
Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions. CoRR (2018)
Varun Shankar, Akil Narayan, Robert M. Kirby
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for solving PDEs on surfaces. J. Comput. Phys. 373 (2018)
Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces. SIAM J. Sci. Comput. 40 (4) (2018)
Varun Shankar, Aaron L. Fogelson
Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations. CoRR (2018)
Varun Shankar, Aaron L. Fogelson
Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations. J. Comput. Phys. 372 (2018)
Vidhi Zala, Varun Shankar, Shankar Prasad Sastry, Robert M. Kirby
Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing. CoRR (2018)
Varun Shankar, Akil Narayan, Robert M. Kirby
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces. CoRR (2018)
Erik Lehto, Varun Shankar, Grady B. Wright
A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces. SIAM J. Sci. Comput. 39 (5) (2017)
Varun Shankar
The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD. J. Comput. Phys. 342 (2017)
Varun Shankar
The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs. CoRR (2016)
Edward J. Fuselier, Varun Shankar, Grady B. Wright
A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations. CoRR (2015)
Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson
A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. J. Sci. Comput. 63 (3) (2015)
Varun Shankar, Sarah D. Olson
Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets. CoRR (2015)
Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson
A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. CoRR (2014)
Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson
Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows CoRR (2013)
Varun Shankar, Grady B. Wright, Aaron L. Fogelson, Robert M. Kirby
A Radial Basis Function (RBF)-Finite Difference Method for the Simulation of Reaction-Diffusion Equations on Stationary Platelets within the Augmented Forcing Method. CoRR (2013)
Varun Shankar, Grady B. Wright, Aaron L. Fogelson, Robert M. Kirby
A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method CoRR (2012)