Vikram V Garg
San Francisco Bay AreaEmail: vikram.v.garg (at) gmail.com
CV
About
I am an applied mathematician and software engineer with strong interests in fluid mechanics and statistics. I create computational methods and algorithms to solve problems in many areas, including, the analysis of complex flows, experimental design, and density estimation. I am a developer of the Finite Element simulation library, libMesh, contributing extensively to its adaptive mesh refinement (AMR) and sensitivity analysis capabilities.
Updates:
- • Mar 2022: Presentation "Leveraging Domain Expertise in Bayesian Experimental Design" Research Presentation.
- • Oct 2021: Presentation "State-of-the-art adjoint capability in libMesh" Update on libMesh adjoints.
- • Oct 2020: Research article "Impact of synthetic arctic argo-type floats in a coupled ocean–sea ice state estimation framework" published in Jtech.
- • July 2019: Research article "Enhanced Functional Evaluation for the Penalty Finite Element Method" published in CAMWA.
- • June 2019: Research article "Adjoint-Consistent Local Enhancement of Functional Evaluation and Error Estimation for Variational Multiscale Formulations" published in CMAME.
- • July 2017: Co-organized mini-symposium "Building Advanced Capabilities in Scientific Software" at USNCCM 2017.
Expertise & Accomplishments
- Building Advanced Simulation Algorithms & Software
• Adjoint based, goal-oriented AMR algorithms for multiscale, multiphysics flow and transport.
• Incorporated state of the art adjoint AMR and sensitivity analysis algorithm in the popular C++ simulation library libMesh.
- Optimization & Inference
• Adjoint based multi-model inference algorithms to guide model adaptivity and experimental design .
• Novel constrained optimization algorithms which mitigate inexact application of complex constraints.
- Statistics & Data Assimilation
• Optimal experimental design strategies for inferring high-dimensional, nonstationary ocean model parameters using R-INLA.
• Density estimation algorithms targeted at inferring heavy tailed distributions without using specialized heuristics.
• First fully flexible incremental Latin Hypercube sampler enabling efficient evaluation of high dimensional response functions.
Publications
- Impact of synthetic arctic argo-type floats in a coupled ocean–sea ice state estimation framework
An T Nguyen, Patrick Heimbach, Vikram V Garg, Victor Ocaña, Craig Lee, Luc Rainville
Journal of Atmospheric and Oceanic Technology, 2020
- Enhanced Functional Evaluation for the Penalty Finite Element Method
Vikram V Garg, Serge Prudhomme
Computers & Mathematics with Applications, 2019
- Adjoint-Consistent Local Enhancement of Functional Evaluation and Error Estimation
Vikram V Garg, Roy H Stogner
Computer Methods in Applied Mechanics and Engineering, 2019
- Model adaptivity for goal-oriented inference using adjoints
Harriet Li, Vikram V Garg, Karen Willcox
Computer Methods in Applied Mechanics and Engineering, 2018
- On the benefit of current and future ALPS data for improving Arctic coupled ocean-sea ice state estimation
An T Nguyen, Victor Ocaña, Vikram V Garg, Patrick Heimbach and others
Oceanography, 2017
- Hierarchical Latin Hypercube Sampling
Vikram V Garg, Roy H Stogner
Journal of the American Statistical Association, 2017
- Minimum local distance density estimation
Vikram V Garg, Luis Tenorio, Karen Willcox
Communications in Statistics-Theory and Methods, 2017
- Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems
Vikram V Garg, Serge Prudhomme, Kris G van der Zee, Graham F Carey
Advanced Modeling and Simulation in Engineering Sciences, 2014
- Flux evaluation in primal and dual boundary-coupled problems
EH van Brummelen, KG van der Zee, VV Garg, S Prudhomme
Journal of Applied Mechanics, 2012
Teaching
- Massachusetts Institute of Technology
Assistant Instructor: Computational Methods in Aeropsace Engineering - Spring 2013 & Spring 2014
- The University of Texas at Austin
Teaching Assistant: Freshman Calculus- Fall 2007 & Spring 2008
Service
- Co-organizer
Mini Symposium on "Adjoints in Computational Software" - USNCCM 2017.
- Reviewer
SIAM Journal on Scientific Computing, Numerische Mathematik, Computers & Mathematics with Applications, Computer Methods in Applied Mechanics & Engineering, Numerical Methods for Partial Differential Equations, International Journal for Numerical Methods in Engineering.
Education
2007 - 2012
Ph.D. in Computational and Applied Mathematics
The University of Texas at Austin
Thesis: Coupled Flow Systems, Adjoint Techniques and Uncertainty Quantification
Advisors: Graham Carey, Serge Prudhomme
2003 - 2007
B.S. in Aerospace Engineering
B.S. in Pure Mathematics
The University of Texas at Austin
GPA: 3.97/4.00
Experience
- Postdoctoral Associate
The University of Texas at Austin 2014-2017.
- Postdoctoral Associate
Massachusetts Institute of Technology 2012-2014.