Utah Digital Twin LabUDTL · University of Utah
Publications

Papers and preprints

Filter by thrust or search by keyword. Links go to arXiv, DOI, or OpenReview where available.

Bold: Varun Shankar · Underlined: lab members (current and former students)

In review

  1. The Frame Kernel Method for Multiscale Operator Learning Branden Frieden, Ryan Whitehead, Keith Ballard, Robert M. Kirby, Varun Shankar
    arXivIn review
  2. A high-order, meshless, Lagrangian–Eulerian RBF-FD method for advection–diffusion–reaction on moving manifolds Matthew Lowery, Grady B. Wright, Varun Shankar
    arXivIn review
  3. Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks Madison Cooley, Ramansh Sharma, Shandian Zhe, Robert M. Kirby, Varun Shankar
    In review
  4. Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar
    arXivIn review
  5. Deep Gaussian Processes for Functional Maps Matthew Lowery, Zhitong Xu, Da Long, Keyan Chen, Daniel S. Johnson, Yang Bai, Varun Shankar, Shandian Zhe
    arXivIn review
  6. Blockchain Compliance: A Framework for Evaluating Regulatory Approaches Ben Charoenwong, Pratik Soni, Varun Shankar, Robert M. Kirby, Jonathan Reiter
    PaperIn review
  7. An Optimal Weighted Least-Squares Method for Operator Learning John Turnage, Matthew Lowery, John Jakeman, Zackary Morrow, Akil Narayan, Varun Shankar
    arXivIn review

2026

  1. Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots Branden Frieden, James M Ferguson, Alan Kuntz, Varun Shankar IEEE International Conference on Robotics and Automation, ICRA, 2026
    arXiv
  2. Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning Matthew Lowery, John Turnage, Zachary Morrow, John D Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar Transactions on Machine Learning Research, 2026
    arXivOpenReview
  3. Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation Madison Cooley, Shandian Zhe, Robert M Kirby, Varun Shankar SIAM Journal on Scientific Computing, 2026
    arXivDOI
  4. A Unified Framework for Efficient Kernel and Polynomial Interpolation Milena Belianovich, Gregory E. Fasshauer, Akil Narayan, Varun Shankar Journal of Approximation Software, 2026
    arXivDOIPaper

2025

  1. Rootfinding and Optimization Techniques for Solving Nonlinear Systems of Equations Arising from Cohesive Zone Models Alberto Cattaneo, Varun Shankar, Michael Ballard AIAA SciTech 2025 Forum, 2025
    arXiv
  2. Ensemble and Mixture-of-Experts DeepONets For Operator Learning Ramansh Sharma, Varun Shankar Transactions on Machine Learning Research, 2025
    arXivOpenReview
  3. HyResPINNs: A Hybrid Residual Physics-Informed Neural Network Architecture Designed to Balance Expressiveness and Trainability Madison Cooley, Robert M. Kirby, Shandian Zhe, Varun Shankar Transactions on Machine Learning Research, 2025
    arXivOpenReview

2024

  1. Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases Madison Cooley, Varun Shankar, Robert M. Kirby, Shandian Zhe Transactions on Machine Learning Research, 2024
    arXivOpenReview
  2. Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis Urban Duh, Varun Shankar, Gregor Kosec Journal of Scientific Computing, 2024
    DOI

2023

  1. Locally Adaptive and Differentiable Regression Mingxuan Han, Chenglong Ye, Varun Shankar, Jeff Phillips Journal of Machine Learning for Modeling and Computing, 2023
    arXivDOI
  2. 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 Journal on Scientific Computing, 2023
    arXivDOI

2022

  1. Accelerated training of physics-informed neural networks (PINNs) using Meshless Discretizations Ramansh Sharma, Varun Shankar NeurIPS, 2022
    arXivDOIPaper
  2. Remaining Challenges in the Application of High-Performance Computing to a Process-To-Performance Pipeline for Textile Composites Keith M. Ballard, Endel Iarve, John Whitcomb, Varun Shankar, Hari Sundar, Lauren Ferguson, Robert M. Kirby, David Mollenhauer Proceedings of the American Society for Composites-Thirty-Seventh Technical Conference, 2022
    DOIPaper
  3. Immersed boundary simulations of cell-cell interactions in whole blood Andrew Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson Journal of Computational Physics, 2022
    arXivDOI
  4. A fine-grained parallelization of the Immersed Boundary method Andrew Kassen, Varun Shankar, Aaron L. Fogelson International Journal of High Performance Computing Applications, 2022
    arXivDOI
  5. Towards an Extrinsic, CG-XFEM approach based on hierarchical enrichments for modeling progressive fracture Keith M. Ballard, Roman Amici, Varun Shankar, Lauren A. Ferguson, M. Braginsky, Robert M. Kirby Computer Methods in Applied Mechanics and Engineering, 2022
    arXivDOI

2021

  1. An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains Varun Shankar, Grady B. Wright, Aaron Fogelson Journal of Computational Physics, 2021
    arXivDOI
  2. Pump efficacy in a two-dimensional, fluid-structure-interaction model of a chain of contracting lymphangions Hallie Elich, Aaron Barrett, Varun Shankar, Aaron L. Fogelson Biomechanics and Modeling in Mechanobiology, 2021
    arXivDOI

2020

  1. A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds Varun Shankar, Grady B. Wright, Akil Narayan SIAM Journal on Scientific Computing, 2020
    arXivDOI
  2. Asymptotic and numerical analysis of a stochastic PDE model of volume transmission Sean Lawley, Varun Shankar SIAM Multiscale Modeling and Simulation, 2020
    arXivDOI

2019

  1. A preliminary assessment of a new XFEM framework for predicting complex fracture Keith M. Ballard, Roman Amici, Varun Shankar, Robert M. Kirby 22nd International Conference on Composite Materials (ICCM22), 2019

2018

  1. Hyperviscosity-based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) discretizations of advection-diffusion equations Varun Shankar, Aaron L. Fogelson Journal of Computational Physics, 2018
    arXivDOI
  2. RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolants (LOI) for Solving PDEs on Surfaces Varun Shankar, Akil Narayan, Robert M. Kirby Journal of Computational Physics, 2018
    arXivDOI
  3. Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces Varun Shankar, Aaron L. Fogelson, Robert M. Kirby SIAM Journal on Scientific Computing, 2018
    arXivDOI
  4. Mesh-free Semi-Lagrangian Methods for Advection on a Sphere using Radial Basis Functions Varun Shankar, Grady B. Wright Journal of Computational Physics, 2018
    arXivDOI
  5. 3-D FDTD Modeling of Electromagnetic Wave Propagation in Magnetized Plasma Requiring Singular Updates to the Current Density Equation Santosh Pokhrel, Varun Shankar, Jamesina J. Simpson IEEE Transactions on Antennas and Propagation, 2018
    DOI
  6. Curvilinear Mesh Rectification using Radial Basis Function Interpolation and Smoothing Vidhi Zala, Varun Shankar, Shankar P. Sastry, Robert M. Kirby Journal of Scientific Computing, 2018
    arXivDOI
  7. Simplified FDTD model of electromagnetic wave propagation in magnetized plasma Santosh Pokhrel, Varun Shankar, Jamesina J. Simpson Applied Computational Electromagnetic Society Symposium [ACES], 2018
    DOI

2017

  1. The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method: A Generalization of RBF-FD Varun Shankar Journal of Computational Physics, 2017
    arXivDOI
  2. A Radial Basis Function (RBF)-Based Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces E. Lehto, Varun Shankar, Grady B. Wright SIAM Journal on Scientific Computing, 2017
    DOI

2016

  1. A High-Order Radial Basis Function (RBF)-Based Leray Projection Method for the Incompressible Stokes Equations Edward J. Fuselier, Varun Shankar, Grady B. Wright Computers and Fluids, 2016
    arXivDOI

2015

  1. 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 Int. J. Numer. Meth. Fluids, 2015
    arXivDOI
  2. Radial Basis Function (RBF)-Based Parametric Models for Open and Closed Curves within the Method of Regularized Stokeslets Varun Shankar, Sarah D. Olson Int. J. Numer. Meth. Fluids, 2015
    arXivDOI

2014

  1. A Radial Basis Function (RBF)-Finite Difference Method for Diffusion and Reaction-Diffusion Equations on surfaces Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson Journal of Scientific Computing, 2014
    arXivDOI
  2. 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 Int. J. Numer. Meth. Fluids, 2014
    arXivDOI

2013

  1. 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 Applied Numerical Mathematics, 2013
    arXivDOI