Andrew Gillette
Computational Mathematician
Center for Applied Scientific Computing
Lawrence Livermore National Laboratory
gillette7 [at] llnl.gov
Andrew Gillette
Computational Mathematician
Center for Applied Scientific Computing
Lawrence Livermore National Laboratory
gillette7 [at] llnl.gov
publications
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→ link to my Google scholar profile
code
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name | dates | description
---- | ---- | ---- | ----
Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning | 2024 - ... | Gaussian processes, radial basis functions, Delaunay interpolants, error bounds, and neural networks playing nicely together.
| | Related paper: Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning
Delaunay Density Diagnostic | 2022 - ... | Assess sampling density of numerical datasets via Delaunay interpolation.
| | Related paper: Data-driven geometric scale detection via Delaunay interpolation
(AM)^2 R: Adaptive Marking Adaptive Mesh Refinement | 2022 - ... | Deploy reinforcement learning to improve hp-adaptive finite element methods.
| | Related paper: Learning robust marking policies for adaptive mesh refinement
talks
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date | title | topic | forum | location
---- | ---- | ---- | ---- | ----
Sep 2023 | The Skeptical Advocate: A role for mathematicians in an AI world | machine learning | invited colloquium | University of Arizona
Aug 2023 | Delaunay interpolation methods for scientific machine learning | machine learning | invited seminar | Los Alamos National Laboratory (virtual)
Jul 2023 | How to treat mesh refinement as a game — and win! — using reinforcement learning | machine learning | Computing Seminar Series | LLNL (virtual)
Mar 2023 | Why are mathematicians jumping on the machine learning bandwagon? | machine learning | DOE Computational Research Leadership Council Seminar | San Francisco State University (virtual)
Feb 2023 | Adaptive Marking for Adaptive Mesh Refinement via Reinforcement Learning | machine learning | SIAM Conference on Computational Science and Engineering | Amsterdam, Netherlands
Feb 2023 | Adaptive Marking for Adaptive Mesh Refinement via Reinforcement Learning | machine learning | invited seminar | Los Alamos National Laboratory (virtual)
Feb 2023 | Why are mathematicians jumping on the machine learning bandwagon? | machine learning | DOE Computational Research Leadership Council Seminar | Alabama State University (virtual)
Jul 2022 | Barycentric coordinates in general dimensions for scientific machine learning | barycentric cooridnates | Computing Seminar Series | LLNL (virtual)
Jun 2022 | Barycentric coordinates in general dimensions | barycentric cooridnates | CSF Workshop on Generalized Barycentric Coordinates | Ascona, Switzerland
Mar 2022 | Data-driven geometric scale detection via Delaunay interpolation | machine learning | WPD/WSC Cognitive Simulation and Machine Learning Workshop | LLNL (virtual)
Feb 2022 | Why are mathematicians jumping on the machine learning bandwagon? | machine learning | DOE Computational Research Leadership Council Seminar | Arizona State University (virtual)
Dec 2021 | Delaunay interpolation diagnostics for model assessment | machine learning | Center for Mathematics and Artificial Intelligence Colloquium | George Mason University (virtual)
Nov 2021 | Why are mathematicians jumping on the machine learning bandwagon? | machine learning | DOE Computational Research Leadership Council Seminar | CSU Fresno (virtual)
Oct 2021 | Delaunay rate check diagnostics for model assessment | machine learning | CASC WIP Seminar | LLNL (virtual)
Jul 2021 | How can you know if your neural network is doing a good job? | machine learning | Computing Seminar Series | LLNL (virtual)
Mar 2021 | Delaunay-Based Assessment of Variational Autoencoders | machine learning | SIAM Conference on Computational Science and Engineering | Fort Worth, TX (virtual)
Feb 2021 | Delaunay-Guided Neural Network Design | machine learning | Colorado State Applied Math Seminar | Colorado State University (virtual)
Jul 2020 | How I Learned to Stop Worrying and Love Machine Learning Research | machine learning | Computing Seminar Series | LLNL (virtual)
Apr 2019 | Basis construction techniques for serendipity-type spaces | serendipity elements | Polytopal Element Methods in Mathematics and Engineering | CIRM, Marseille, France
Mar 2019 | How to speed up your tensor product finite element code without really trying | serendipity elements | AMS Spring Central and Western Joint Sectional Meeting | University of Hawaii at Manoa
Dec 2018 | Structure Preservation in (Trimmed) Serendipity Finite Element Methods | serendipity elements | Canadian Math Society Winter Meeting | Vancouver, Canada
Nov 2018 | (Trimmed) Serendipity Finite Element Methods in Theory and Practice | serendipity elements | Computational Mathematics Seminar | Louisiana State University
Sep 2018 | Serendipity Elements: Old and New | finite element analysis | Geometric and Image Data Sciences Workshop | UT Austin
Sep 2018 | Polynomial Differential Forms for Efficient Finite Element Methods | finite element analysis | invited colloquium | Baylor University
Jul 2018 | Computational Finite Element Differential Forms on Quadrilateral Meshes | finite element analysis | SIAM Annual Meeting | Portland, OR
Mar 2018 | From Squares and Cubes to Quads and Hexes: Recent Advances in Conforming Finite Elements | finite element analysis | CCOM Seminar | UC San Diego
Jan 2018 | An Introduction to Trimmed Serendipity Finite Element Spaces | serendipity elements | AMS-MAA Joint Meetings | San Diego, CA
Sep 2017 | A Plethora of Basis Functions for Quadrilaterals and Hexahedra | finite element analysis | ENUMATH 2017 | Voss, Norway
Sep 2017 | Decompositions of (Trimmed) Serendipity Spaces | serendipity elements | ENUMATH 2017 | Voss, Norway
Jul 2017 | A "Fifth Column" for the Periodic Table of Finite Elements | serendipity elements | Polytopal Element Methods in Mathematics and Engineering | Milan, Italy
Apr 2017 | An algebraist and a numerical analyst walk into a bar... | finite element analysis | Research Training Group Talks | University of Arizona
Mar 2017 | Finite Element Methods: Applied theory and theoretical applications | finite element analysis | Recruitment Workshop Talk | University of Arizona
Oct 2016 | A New Family of Conforming Finite Elements on Cubical Meshes | serendipity elements | Computaional Math Seminar | University of Pittsburgh
Sep 2016 | A "Fifth Column" for Finite Elements | serendipity elements | Modeling and Computation Seminar | University of Arizona
Jun 2016 | The Serendipity Pyramid Finite Element | serendipity elements | Mathematics of Finite Elements and Applications 2016 | Brunel University London
Jun 2016 | Generalized barycentric coordinates for degenerate geometry in FEM | finite element analysis | Mathematics of Finite Elements and Applications 2016 | Brunel University London
Jan 2016 | An Introduction to Research in Finite Element Exterior Calculus | finite element analysis | Research Training Group Talks | University of Arizona
Jan 2016 | Polytopal Finite Element Methods: Theory and Application | finite element analysis | CIMAT Meeting | Guanajuato, Mexico
Dec 2015 | The State of the Art in Polytopal Finite Element Methods | finite element analysis | SIAM Conference on Analysis of PDEs | Scottsdale, AZ
Nov 2015 | Polytopal Element Methods: What, Why, and Where? | finite element analysis | Modeling and Computation Seminar | University of Arizona
Nov 2015 | The Rapidly Growing Zoo of Polytopal Finite Element Methods | finite element analysis | UC Berkeley Applied Math Seminar | UC Berkeley
Jul 2015 | What is a good linear finite element... on a generic polytope? | finite element analysis | 13th US National Congress on Computational Mechanics | San Diego, CA
Mar 2015 | Multiscale biological modeling: Using every area of mathematics that you can imagine | biological modeling | Recruitment Workshop Talk | University of Arizona
Mar 2015 | A Brief Introduction to Splines on Triangulations | spline functions | Research Training Group Talks | University of Arizona
Nov 2014 | Modern Directions in Finite Element Theory: Polytope Meshes and Serendipity Methods | barycentric cooridnates | Portland State Math Colloquium | Portland, OR
Oct 2014 | H(curl) and H(div) Elements on Polytopes from Generalized Barycentric Coordinates | barycentric cooridnates | Finite Element Circus 2014 | Minneapolis, MN
Sep 2014 | Multiscale Diffusion Modeling in Charged and Crowded Biological Environments | biological modeling | Duke Math Biology Colloquium | Durham, NC
Jun 2014 | Nodal Bases for the Serendipity Family of Finite Elements | serendipity elements | International Conference on Spectral and High Order Methods 2014 | Salt Lake City, UT
Jun 2014 | Gradient Bounds for Wachspress Coordinates on Polytopes | barycentric coordinates | 8th International Conference on Curves and Surfaces | Paris, France
Jun 2014 | Generalized Barycentric Coordinate Finite Element Methods on Polytope Meshes | finite element analysis | invited seminar | CERMICS, Paris, France
Apr 2014 | Polygonal, Polyhedral, and Serendipity Finite Element Methods | serendipity elements | Computational and Applied Math Seminar | Arizona State University
Mar 2014 | Cardiac Diffusion Modeling via Homogenization of the Smoluchowski Equation | biological modeling | Quantitative Biology Colloquium | University of Arizona
Jan 2014 | Research Problems in Finite Element Theory: Analysis, Geometry, and Applications | serendipity elements | Research Training Group Talks | University of Arizona
Jan 2014 | Serendipity Basis Functions for Any Degree in Any Dimension | serendipity elements | Isogeometric Analysis 2014 | Austin, TX
Oct 2013 | Computation of Macroscopic Diffusion Constants via Homogenization of the Smoluchowski Equation | biological modeling | Modeling and Computation Seminar | University of Arizona
Sep 2013 | An Introduction to Finite Elements or How I Learned to Stop Worrying and Love Functional Analysis | finite element analysis | Applied Math Brown Bag Seminar | University of Arizona
Sep 2013 | Cardiac Electrophysiology Modeling with Serendipity Finite Elements | serendipity elements | Modeling and Computation Seminar | University of Arizona
May 2013 | Analysis and Application of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited seminar | University of Oslo, Norway
May 2013 | Serendipity Finite Element Methods for Cardiac Electrophysiology Models | serendipity elements | Workshop on Advancing Numerical Technologies in the Cardiac Domain | Simula Research Laboratory, Oslo, Norway
Apr 2013 | Basis Functions for Serendipity Finite Element Methods | serendipity elements | 14th International Conference on Approximation Theory | San Antonio, TX
Mar 2013 | An Introduction to Hermite Serendipity Finite Element Methods | serendipity elements | invited colloquium | Cal Poly Pomona
Feb 2013 | Cubic Serendipity Basis Functions for Isogeometric Analysis | serendipity elements | Advances in Computational Mechanics / Tom Hughes' 70th Birthday | San Diego, CA
Feb 2013 | Analysis and Applications of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited colloquium | Southern Methodist University
Feb 2013 | Hermite Polynomials and Geometric Decompositions | serendipity elements | invited undergraduate seminar | Loyola Marimount University
Feb 2013 | Analysis and Applications of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited colloquium | University of Arizona
Jan 2013 | Geometric Decomposition of Serendipity Finite Element Spaces | serendipity elements | AMS-MAA Joint Meetings | San Diego, CA
Oct 2012 | Fewer Degrees of Freedom, Same Convergence Rate: Recent progress in serendipity finite element methods | serendipity elements | invited seminar | Georgia Tech
Aug 2012 | Using FEniCS for Finite Element Methods | finite element software | tutorial at National Biomedical Computation Resource Summer Institute | UC San Diego
Jul 2012 | Error Estimates for Generalized Barycentric Coordinate Finite Element Methods | barycentric coordinates | plenary lecture at NSF Workshop on Barycentric Coordinates | Columbia University
Jul 2012 | The Geometry of Interpolation Error Estimates for Isogeometric Analysis | isogeometric analysis | SIAM Annual Meeting | Minneapolis, MN
Dec 2011 | Finite Element Exterior Calculus for Evolution Problems | finite element analysis | ICES / CVC Seminar | UT Austin
Nov 2011 | Finite Element Clifford Algebra: A New Toolkit for Evolution Problems | finite element analysis | SIAM Conference on Analysis of PDEs | San Diego, CA
Nov 2011 | Discrete Exterior Calculus and Polygonal Finite Elements | discrete exterior calculus | Workshop on Geometric Numerical Methods for PDEs | UC San Diego
Oct 2011 | Geometric Criteria for Generalized Barycentric Finite Elements | barycentric coordinates | SIAM-ACM Joint Conference on Geometric and Physical Modeling | Orlando, FL
Oct 2011 | Generalized Barycentric Coordinates for Polygonal Finite Elements | barycentric coordinates | CCOM Seminar | UC San Diego
May 2011 | Stability of Dual Discretization Methods for Partial Differential Equations | finite element analysis | thesis defense | UT Austin
Feb 2011 | Modeling Electrical Activity in Neurons with Discrete Calculus | biological modeling | undergraduate math club | UT Austin
Jan 2011 | Conforming Vector Interpolation Functions for Polyhedral Meshes | discrete exterior calculus | invited seminar | Los Alamos National Laboratory, NM
Jan 2011 | Dual Interpolants for Finite Element Methods | finite element analysis | AMS-MAA Joint Meetings | New Orleans, LA
Nov 2010 | Compatibility Conditions for Dual Discretization Methods | discrete exterior calculus | CVC Group Meeting | UT Austin
Sep 2010 | A Generalization for Stable Mixed Finite Elements | discrete exterior calculus | ACM Symposium on Solid and Physical Modeling | Haifa, Israel
Jun 2010 | Real Algebraic Finite Elements and deRham Cohomology | discrete exterior calculus | invited seminar | KAUST, Saudi Arabia
Apr 2010 | DEC-deRham Conformity for Mixed Finite Element Methods | discrete exterior calculus | Demkowicz Group Meeting | UT Austin
Apr 2010 | Voronoi Diagrams: Fencing Out Your Neighbors | voronoi diagrams | Sunday Math Circle | UT Austin
Apr 2010 | Cohomology Stability Criteria for Mixed Finite Element Methods | discrete exterior calculus | TACG Seminar | UT Austin
Mar 2010 | New Model Stability Criteria for Mixed Finite Elements | discrete exterior calculus | CVC Group Meeting | UT Austin
Oct 2009 | Multi-scale Modeling of Electric Activity of Spiny Dendrites in the Hippocampus | biological modeling | AMS Fall Central Section Meeting | Baylor University
Jun 2009 | Automated Neuronal Reconstruction: Current Challenges and Proposed Quantification | biolgoical modeling | CVC Group Meeting | UT Austin
Feb 2009 | Geometric Discretization of Stress and Elasticity | discrete exterior calculus | CVC Group Meeting | UT Austin
Jan 2009 | Applications of the Hodge Decomposition to Biological Structure and Function Modeling | biological modeling | AMS-MAA Joint Meetings | Washington, DC
Dec 2008 | Applications of the Hodge Decomposition to Biological Structure and Function Modeling | biological modeling | candidacy exam | UT Austin
Oct 2008 | Quality Meshing of a Forest of Branching Structures | biological modeling | 17th International Meshing Roundtable | Pittsburgh, PA
Sep 2008 | Discrete Mathematics for Molecular Models | biological modeling | undergraduate math club | UT Austin
Aug 2008 | Topology-controlled Stable Function Modeling for Biology | biological modeling | CVC Group Meeting | UT Austin
Apr 2008 | Persistent Homology: A Tool For Molecular Modeling | biological modeling | Junior Topology Seminar | UT Austin
Jan 2008 | The State of Affairs in Protein Modeling | biological modeling | CVC Group Meeting | UT Austin
Nov 2007 | Critical Problems with Critical Points | computational geometry / topology | CVC Group Meeting | UT Austin
Oct 2007 | Efficient Delaunay Mesh Generation From Sampled Scalar Functions | computational geometry / topology | 16th International Meshing Roundtable | Seattle, WA
Mar 2007 | Topology Based Selection and Curation of Level Sets | computational geometry / topology | Topology In Visualization conference | Grimma, Germany
Feb 2007 | An Unstable Instance of the Finite Element Method | finite element analysis | CVC Group Meeting | UT Austin
posters
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year | title | authors
---- | ---- | ---- | ----
2023 | Multi-Objective Adaptive Mesh Refinement Using Reinforcement Learning | J. Zvonek, A. Gillette
| SIAM Conference on Computational Science and Engineering [pdf]
2021 | Serendipity and Trimmed Serendipity Elements in Firedrake | J. Crum, A. Gillette,
conferences
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→ Upcoming conferences listed in intro + news section
Defense and Aerospace Test and Analysis Workshop, Alexandria, VA, April 2024.
SIAM Conference on Computational Science and Engineering, Amsterdam, Netherlands, Feb 2023.
SIAM Conference on Mathematics of Data Science, San Diego, CA, September 2022.
Advanced Research Directions in AI for Science and Security, Davis, CA, July 2022.
CSF Workshop on Generalized Barycentric Coordinates, Monte Verita, Ascona, Switzerland, June 2022.
SIAM Conference on Computational Science and Engineering, Fort Worth, TX (virtual), March 2021.
Bay Area Scientific Computing Day 2019, Lawrence Berkeley National Laboratory, Berkeley, CA, December 2019.
Polytopal Element Methods in Mathematics and Engineering (PoEMs 2019), Centre International de Rencontres Mathematiques, Marseille, France, April 2019.
AMS Spring Central and Western Joint Sectional Meeting, Honolulu, HI, March 2019.
Canadian Mathematical Society Winter Meeting, Vancouver, Canada, Dec 2018.
Geometric & Image Data Sciences: Big Data Analysis, Graphics & Visualization, Austin, TX, September 2018.
World Congress on Computational Mechanics, New York, NY, July 2018.
SIAM Annual Meeting, Portland, OR, July 2018.
AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2018.
Organizer for AMS Special Session on Mathematics of Gravitational Wave Science
Speaker in AMS Special Session on Recent Trends in Analysis of Numerical Methods of Partial Differential Equations
European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway, September 2017.
Polytopal Element Methods in Mathematics and Engineering (PoEMs 2017), Milan, Italy, July 2017.
CIMAT-UA Workshop and Rabi Fest, Tucson, AZ, March 2017.
SIAM Conference on Computational Science and Engineering, Atlanta, GA, February 2017.
I.H.P. Quarter on Numerical Methods for Partial Differential Equations, Institut Henri Poincaré, Paris, France, September 2016.
Mathematics of Finite Elements and Applications, Brunel University London, England, June 2016.
Advances in Mathematics of Finite Elements (Ivo Babuska 90th Birthday Conference), Austin, TX, March 2016.
SIAM Conference on Analysis of Partial Differential Equations, Scottsdale, AZ, December 2015.
Polytopal Element Methods in Mathematics and Engineering (PoEMs 2015), Atlanta, GA, October 2015.
Workshop Co-organizer; support from conference grant DMS-1542183 from the National Science Foundation.
13th US National Congress on Computational Mechanics, San Diego, CA, July 2015.
Co-organizer for mini-symposium Polygonal and Polyhedral Discretizations in Computational Mechanics
9th International Conference on Geometric Modeling and Processing, Lugano, Switzerland, June 2015.
Advanced Numerical Methods in the Mathematical Sciences, Texas A&M University, May 2015.
SIAM Conference on Computational Science and Engineering, Salt Lake City, UT, March 2015.
Finite Element Circus 2014, Minneapolis, MN, October 2014.
IMA Special Workshop: Structure-Preserving Discretizations of Partial Differential Equations, Minneapolis, MN, October 2014.
International Conference on Spectral and High Order Methods, Salt Lake City, UT, June 2014.
8th International Conference on Curves and Surfaces, Paris, France, June 2014.
Robust Discretization and Fast Solvers for Computable Multi-Physics Models, ICERM, Providence, RI, May 2014.
Program in Applied Mathematics 35th Anniversary Meeting, Tucson, AZ, April 2014.
Isogeometric Analysis 2014, Austin, TX, January 2014.
IMA Workshop: Modern Applications of Homology and Cohomology, Minneapolis, MN, October 2013.
14th International Conference on Approxmation Theory, San Antonio, TX, April 2013.
Advances in Computational Mechanics - Celebrating the 70th Birthday of Thomas J.R. Hughes, San Diego, CA, February 2013.
Workshop on Geometric Numerical Methods for PDE: FEEC + AFEM @ UCSD , San Diego, CA, January 2013.
AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2013.
Cardiac Physiome Workshop, San Diego, CA, October 2012.
SIAM Conference on the Life Sciences, San Diego, CA, August 2012.
National Biomedical Computation Resource Summer Institute (Instructor), UC San Diego, August 2012.
NSF Workshop on Barycentric Coordinates in Geometry Processing and Finite/Boundary Element Methods, New York, NY, July 2012.
SIAM Annual Meeting, Minneapolis, MN, July 2012.
NSF-CBMS Conference: Finite Element Exterior Calculus, ICERM, Providence, RI, June 2012.
SIAM Conference on Analysis of Partial Differential Equations, San Diego, CA, November 2011.
Workshop on Geometric Numerical Methods for PDE, San Diego, CA, November 2011.
SIAM-ACM Joint Conference on Geometric and Physical Modeling, Orlando, FL, October 2011.
Finite Element Rodeo 2011, College Station, TX, February 2011.
Isogeometric Analysis 2011: Integrating Design and Analysis, Austin, TX, January 2011.
AMS-MAA Joint Mathematics Meetings, New Orleans, LA, January 2011.
IMA Workshop: Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, Minneapolis, MN, November 2010.
ACM Symposium on Solid and Physical Modeling, Haifa, Israel, September 2010.
Algorithms in MacroMolecular Modeling Conference, Austin, TX, November 2009.
AMS Fall Central Section Meeting, Waco, TX, October 2009.
SIAM-ACM Joint Conference on Geometric and Physical Modeling, San Francisco, CA, October 2009.
Summer School Workshop on Multivariate Splines and Their Applications, Athens, GA, May 2009.
Mathematical Aspects of Imaging, Modelling and Visualization in Multiscale Biology, Austin, TX, March 2009. (Organizer)
AMS-MAA Joint Mathematics Meetings, Washington, DC, January 2009.
17th International Meshing Roundtable, Pittsburgh, PA, October 2008.
IMA Tutorial: Mathematics of Proteins, Minneapolis, MN, January 2008.
16th International Meshing Roundtable, Seattle, WA, October 2007.
Topology in Visualization, Grimma, Germany, March 2007.
AMS-MAA Joint Mathematics Meetings, San Antonio, TX, January 2006.
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Program Co-chair and Guest Editor of the associated Special Issue of Computer Aided Geometric Design
Presented a poster that appeared in the Minisyposterium on Mixed Finite Element Methods
Organizer for AMS Special Session on Finite Element Exterior Calculus and Applications
Organizer for session on Computational Biological Modeling at the Interface of Molecular Simulation and Continuum Diffusion
Organizer and speaker for AMS Special Session on Mathematical Models of Biological Structures and Function