A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method - Varun Shankar; Grady B. Wright; Aaron L. Fogelson; Robert M. Kirby (CoRR, 2012)

A Radial Basis Function (RBF)-Finite Difference Method for the Simulation of Reaction-Diffusion Equations on Stationary Platelets within the Augmented Forcing Method. - Varun Shankar; Grady B. Wright; Aaron L. Fogelson; Robert M. Kirby (CoRR, 2013)

Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows - Varun Shankar; Grady B. Wright; Robert M. Kirby; Aaron L. Fogelson (CoRR, 2013)

Radial Basis Function-Based Numerical Methods for the Simulation of Platelet Aggregation. - Varun Shankar (2014)

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 (CoRR, 2015)

Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets. - Varun Shankar; Sarah D. Olson (CoRR, 2015)

A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. - Varun Shankar; Grady B. Wright; Robert M. Kirby; Aaron L. Fogelson (J. Sci. Comput., 2015)

The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs. - Varun Shankar (CoRR, 2016)

The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD. - Varun Shankar (J. Comput. Phys., 2017)

A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces. - Erik Lehto; Varun Shankar; Grady B. Wright (SIAM J. Sci. Comput., 2017)

Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces. - Varun Shankar; Robert M. Kirby; Aaron L. Fogelson (CoRR, 2018)

Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations. - Varun Shankar; Aaron L. Fogelson (J. Comput. Phys., 2018)

RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for solving PDEs on surfaces. - Varun Shankar; Akil Narayan 001; Robert M. Kirby (J. Comput. Phys., 2018)

Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions. - Varun Shankar; Grady B. Wright (J. Comput. Phys., 2018)

Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing. - Vidhi Zala; Varun Shankar; Shankar P. Sastry; Robert M. Kirby (J. Sci. Comput., 2018)

Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces. - Varun Shankar; Robert M. Kirby; Aaron L. Fogelson (SIAM J. Sci. Comput., 2018)

Asymptotic and Numerical Analysis of a Stochastic PDE Model of Volume Transmission. - Sean D. Lawley; Varun Shankar (Multiscale Model. Simul., 2020)

A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. - Varun Shankar; Grady B. Wright; Akil Narayan 001 (SIAM J. Sci. Comput., 2020)

Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture. - M. Keith Ballard; Roman Amici; Varun Shankar; Lauren A. Ferguson; Michael Braginsky; Robert M. Kirby (CoRR, 2021)

An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains. - Varun Shankar; Grady B. Wright; Aaron L. Fogelson (J. Comput. Phys., 2021)

Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations. - Ramansh Sharma; Varun Shankar (NeurIPS, 2022)

A fine-grained parallelization of the immersed boundary method. - Andrew T. Kassen; Varun Shankar; Aaron L. Fogelson (Int. J. High Perform. Comput. Appl., 2022)

Immersed boundary simulations of cell-cell interactions in whole blood. - Andrew T. Kassen; Aaron Barrett; Varun Shankar; Aaron L. Fogelson (J. Comput. Phys., 2022)

Differentiable Turbulence. - Varun Shankar; Romit Maulik; Venkatasubramanian Viswanathan (CoRR, 2023)

Importance of equivariant and invariant symmetries for fluid flow modeling. - Varun Shankar; Shivam Barwey; Zico Kolter; Romit Maulik; Venkatasubramanian Viswanathan (CoRR, 2023)

Differentiable Turbulence II. - Varun Shankar; Romit Maulik; Venkatasubramanian Viswanathan (CoRR, 2023)

Locally Adaptive and Differentiable Regression. - Mingxuan Han; Varun Shankar; Jeff M. Phillips; Chenglong Ye (CoRR, 2023)

Differentiable physics-enabled closure modeling for Burgers' turbulence. - Varun Shankar; Vedant Puri; Ramesh Balakrishnan; Romit Maulik; Venkatasubramanian Viswanathan (Mach. Learn. Sci. Technol., 2023)

MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces. - Grady B. Wright; Andrew M. Jones; Varun Shankar (SIAM J. Sci. Comput., 2023)

Multiscale graph neural network autoencoders for interpretable scientific machine learning. - Shivam Barwey; Varun Shankar; Venkatasubramanian Viswanathan; Romit Maulik (J. Comput. Phys., 2023)

Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation. - Madison Cooley; Shandian Zhe; Robert M. Kirby; Varun Shankar (CoRR, 2024)

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning. - Matthew Lowery; John Turnage; Zachary Morrow; John D. Jakeman; Akil Narayan 001; Shandian Zhe; Varun Shankar (CoRR, 2024)

HyResPINNs: Adaptive Hybrid Residual Networks for Learning Optimal Combinations of Neural and RBF Components for Physics-Informed Modeling. - Madison Cooley; Robert M. Kirby; Shandian Zhe; Varun Shankar (CoRR, 2024)

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis. - Urban Duh; Varun Shankar; Gregor Kosec (J. Sci. Comput., 2024)

Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases. - Madison Cooley; Varun Shankar; Mike Kirby; Shandian Zhe (Trans. Mach. Learn. Res., 2025)

Ensemble and Mixture-of-Experts DeepONets For Operator Learning. - Ramansh Sharma; Varun Shankar (Trans. Mach. Learn. Res., 2025)

Rootfinding and Optimization Techniques for Solving Nonlinear Systems of Equations Arising from Cohesive Zone Models. - Alberto Cattaneo; Varun Shankar; M. Keith Ballard (CoRR, 2025)