Nathaniel Albert Trask

Computational Mathematics

Author profile picture

Computational Mathematics

natrask@sandia.gov

(505) 844-6016

Sandia National Laboratories, New Mexico
P.O. Box 5800
Albuquerque, NM 87185-1320

Biography

I am a senior member of technical staff in the computational mathematics department in the Center for Computing Research at the Computer Science Research Institute at Sandia National Laboratories.

My research focuses on structure preservation in scientific machine learning and novel meshfree discretizations for PDEs. I have a background in applied mathematics and mechanical engineering, and am particularly interested in developing rigorous mathematical tools to solve practical problems in multiscale and multiphysics problems.

Education

Professional Experience

  • 2018-present Senior Member of Technical Staff, Computational Mathematics Department
  • 2016-2018 National Science Foundational Mathematical Sciences Postdoctoral Fellow
  • 2016 Visiting Professor, Division of Applied Mathematics, Brown University 2009-2016 CFD Consulting Engineer, Self-employed

Education

  • 2016 PhD, Division of Applied Mathematics, Brown University
  • 2012 MSc, Division of Applied Mathematics, Brown University
  • 2010 MSc, Mechanical Engineering, University of Massachusetts
  • 2008 Dual BSc, Mechanical Engineering and Mathematics, University of Massachusetts

Publications

Eric Christopher Cyr, Nathaniel Albert Trask, Amelia Henriksen, Carianne Martinez, (2022). A Two-Level Scheme for Training Partition of Unity Networks 27th International Domain Decomposition Conference Document ID: 1584854

Elizabeth Armstrong, Michael Alan Hansen, Robert C. Knaus, Nathaniel Albert Trask, John C. Hewson, James Sutherland, (2022). Accurate Compression of Tabulated Chemistry Models with Partition of Unity Networks Combustion Science and Technology Document ID: 1562419

Andy Huang, Nathaniel Albert Trask, Xujiao Gao, Shahed Reza, Ravi Ghanshyam Patel, Christopher Brissette, Xiaozhe Hu, (2022). Continuum semiconductor physics model compression via Data-driven Discrete Exterior Calculus 8th European Congress on Computational Methods in Applied Sciences and Engineering Document ID: 1539595

Khemraj Shukla, Mengjia Xu, Nathaniel Albert Trask, George Karniadakis, (2022). Scalable algorithms for physics-informed neural and graph networks Data Centric Engineering https://www.osti.gov/search/identifier:1872036 Document ID: 1539305

Ruben Villarreal, Thomas Anthony Catanach, Reese E. Jones, Nathaniel Albert Trask, Sharlotte LorraineBolyard Kramer, Nikolaos Vlassis N., WaiChing Sun, (2022). Reinforcement learning for material calibration via kalman filter estimation USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling Document ID: 1527865

Elizabeth Armstrong, Michael Alan Hansen, Robert C. Knaus, Nathaniel Albert Trask, John C. Hewson, James Sutherland, (2022). Improving chemistry tabulation with partition of unity networks 18th International Conference on Numerical Combustion Document ID: 1517516

Nathaniel Albert Trask, (2022). Structure preserving machine learning for data-driven multiscale/multiphysics modeling Stanford engineering seminar Document ID: 1493565

Elizabeth Armstrong, Michael Alan Hansen, Robert C. Knaus, Nathaniel Albert Trask, John C. Hewson, James Sutherland, (2022). Improving Chemistry Tabulation with Partition of Unity Networks 18th International Conference on Numerical Combustion Document ID: 1448965

Nathaniel Albert Trask, (2022). Physics-informed Multimodal Autoencoders (PIMA) High-throughput science through modal fusion crunch webinar Document ID: 1438448

Elizabeth Armstrong, Michael Alan Hansen, Robert C. Knaus, Nathaniel Albert Trask, John C. Hewson, James Sutherland, (2022). Accurate Compression of Tabulated Chemistry Models with Partition of Unity Networks 39th International Symposium on Combustion Document ID: 1416233

Paul Allen Kuberry, Mauro Perego, Nathaniel Albert Trask, Pavel B. Bochev, (2021). Remapping native fields for climate applications 15th World Congress on Computational Mechanics (WCCM-XV) Document ID: 1392901

David John Littlewood, Mitchell Wood, David Montes de Oca Zapiain, Sivasankaran Rajamanickam, Nathaniel Albert Trask, (2021). Sandia / IBM Discussion on Machine Learning for Materials Applications https://www.osti.gov/search/identifier:1828106 Document ID: 1370204

Nathaniel Albert Trask, (2021). Structure preserving machine learning for data-driven multiscale/multiphysics modeling UPenn Engineering department colloquium Document ID: 1369341

Andy Huang, Nathaniel Albert Trask, Xujiao Gao, Shahed Reza, Ravi Ghanshyam Patel, Christopher Brissette, Xiaozhe Hu, (2021). Machine learning of Physics-Informed Graph Neural Networks from TCAD models Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology (IACM conference) 2021 Document ID: 1368329

Nathaniel Albert Trask, (2021). Discovery of structure-preserving finite element spaces for multiscale Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology Document ID: 1368335

Nathaniel Albert Trask, Marta D’Elia, David John Littlewood, Stewart A. Silling, Jeremy Trageser, Michael R. Tupek, (2021). ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization https://www.osti.gov/search/identifier:1820006 Document ID: 1357213

Andy Huang, Xujiao Gao, Shahed Reza, Nathaniel Albert Trask, Ian Zachary Wilcox, Candace Pauline Diaz, Ravi Ghanshyam Patel, (2021). Machine learning surrogates of high-fidelity electrical models REHEDS External Review Document ID: 1344617

Nathaniel Albert Trask, (2021). A data-driven exterior calculus for model discovery Usacm Document ID: 1342926

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mitchell Wood, Eric Christopher Cyr, (2021). Modal Operator Regression for Extracting Nonlocal Continuum Models Usnccm16 Document ID: 1342937

Eric Christopher Cyr, Mamikon Gulian, Kookjin Lee (ASU), Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs Fomics-dadsi Seminars On Scientific Learning https://www.osti.gov/search/identifier:1872708 Document ID: 1319002

Nathaniel Albert Trask, (2021). Structure preserving architectures for SciML Philms webinar https://www.osti.gov/search/identifier:1872183 Document ID: 1318613

Barun Das, Masoud Behzadinasab, Nathaniel Albert Trask, John Foster, (2021). ASCeND: ASymptotically Compatible Strong Form Foundations for Nonlocal Discretization Sandia Academic Alliance Spring 2021 UT Austin LDRD Virtual Poster Session https://www.osti.gov/search/identifier:1862184 Document ID: 1293266

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Eric Christopher Cyr, (2021). Multiscale training for Physics-informed Neural Networks Copper Mountain Conference On Multigrid Methods https://www.osti.gov/search/identifier:1861255 Document ID: 1292759

Andy Huang, Nathaniel Albert Trask, Christopher Brissette, Xiaozhe Hu, (2021). Greedy Fiedler Spectral Partitioning for Data-driven Discrete Exterior Calculus Association for the Advancement of Artificial Intelligence – Machine Learning for the Physical Sciences (AAAI-MLPS) 2021 https://www.osti.gov/search/identifier:1859685 Document ID: 1291951

Nathaniel Albert Trask, (2021). Making physics-informed ML work Informal presentation for ML reading group at LANL https://www.osti.gov/search/identifier:1856302 Document ID: 1281731

Nathaniel Albert Trask, (2021). Partition of unity networks: deep hp-approximation AAAI MLPS virtual meeting https://www.osti.gov/search/identifier:1856303 Document ID: 1281781

Nathaniel Albert Trask, (2021). Convergent and structure preserving architectures for SciML USACM UQ webinar https://www.osti.gov/search/identifier:1856094 Document ID: 1281674

Mamikon Gulian, Ravi Ghanshyam Patel, Nathaniel Albert Trask, Eric Christopher Cyr, (2021). A block coordinate descent optimizer for classification problems exploiting convexity Aaai-mlps 2021 https://www.osti.gov/search/identifier:1855748 Document ID: 1281385

Nathaniel Albert Trask, (2021). Northwestern tutorial Tutorial lecture for engineering group at Northwestern https://www.osti.gov/search/identifier:1854536 Document ID: 1280614

Andy Huang, Nathaniel Albert Trask, Xujiao Gao, Shahed Reza, Ian Zachary Wilcox, Candace Pauline Diaz, (2021). Extraction of Data-Driven Compact Models from High-Fidelity Semiconductor Simulations with Topological Data Analysis SIAM Conference on Computional Science and Engineering 2021 https://www.osti.gov/search/identifier:1854316 Document ID: 1280076

Nathaniel Albert Trask, (2021). Designing convergent and structure preserving architectures for SciML One World ML virtual meeting https://www.osti.gov/search/identifier:1854079 Document ID: 1280266

Nathaniel Albert Trask, (2021). Designing convergent and structure preserving architectures for SciML University of Texas El Paso Department Seminar https://www.osti.gov/search/identifier:1853849 Document ID: 1279787

Nathaniel Albert Trask, (2021). A data-driven exterior calculus for model discovery Siam Cse https://www.osti.gov/search/identifier:1853865 Document ID: 1280071

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mitchell Wood, Eric Christopher Cyr, (2021). A Physics-Informed Operator Regression Framework for Extracting Data-Driven Continuum Models Siam Cse21 https://www.osti.gov/search/identifier:1853856 Document ID: 1279866

Indu Manickam, Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mitchell Wood, Myoungkyu NMN Lee, Ignacio Tomas, Eric Christopher Cyr, (2021). Thermodynamically consistent physics-informed neural networks for hyperbolic systems SIAM Conference on Computational Science and Engineering https://www.osti.gov/search/identifier:1847572 Document ID: 1279762

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs SIAM Conference on Computational Science and Engineering (CSE21) https://www.osti.gov/search/identifier:1847582 Document ID: 1279963

Huaiqian You, Xin Yang Lu, Nathaniel Albert Trask, Yue Yu, (2021). An Asymptotically Compatible Approach For Neumann-type Boundary Condition On Nonlocal Problems Esaim https://www.osti.gov/search/identifier:1769929 Document ID: 1279586

Yue Yu, Huaiqian You, Nathaniel Albert Trask, (2021). An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture Computer Methods in applied mechanics and engineering https://www.osti.gov/search/identifier:1769919 Document ID: 1268870

Lee Kookjin, Nathaniel Albert Trask, Ravi Ghanshyam Patel, Mamikon Gulian, Eric Christopher Cyr, (2020). Partition of unity networks: data-driven meshfree hp-approximation AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences https://www.osti.gov/search/identifier:1835970 Document ID: 1243888

Ben Gross, Paul Allen Kuberry, Nathaniel Albert Trask, Paul Atzberger, (2020). Meshless Methods for Manifolds GMLS Approximations of Hydrodynamic Responses in Curved Fluid Interfaces Wccm 2020 https://www.osti.gov/search/identifier:1834284 Document ID: 1243206

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mitchell Wood, Eric Christopher Cyr, (2020). Learning continuum-scale models from micro-scale dynamics via Operator Regression 14th World Congress in Computational Mechanics https://www.osti.gov/search/identifier:1834283 Document ID: 1243116

Nathaniel Albert Trask, (2020). A data-driven exterior calculus for model discovery Uncertainty Management and Machine Learning in Engineering Applications Document ID: 1232423

Nathaniel Albert Trask, (2020). A data-driven exterior calculus for model discovery Princeton Plasma Physics Laboratory Seminar https://www.osti.gov/search/identifier:1833914 Document ID: 1232465

Carianne Martinez, Jessica Eileen Jones, Drew Levin, Nathaniel Albert Trask, Patrick D. Finley, (2020). Physics-Informed Machine Learning for Epidemiological Models https://www.osti.gov/search/identifier:1706217 Document ID: 1220076

Paul Allen Kuberry, Nathaniel Albert Trask, Jacob Koester, Pavel B. Bochev, (2020). Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids (REBAR) International Mechanical Engineering Congress & Exposition (IMECE) 2020 https://www.osti.gov/search/identifier:1822641 Document ID: 1207911

Paul Allen Kuberry, Pavel B. Bochev, Jacob Koester, Nathaniel Albert Trask, (2020). Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids: LDRD Final Report https://www.osti.gov/search/identifier:1669732 Document ID: 1196977

Xujiao Gao, Andy Huang, Nathaniel Albert Trask, Shahed Reza, (2020). Physics-Informed Graph Neural Network for Circuit Compact Model Development International Conference on Simulation of Semiconductor Processes and Devices (SISPAD) 2020 https://www.osti.gov/search/identifier:1820261 Document ID: 1196143

Xujiao Gao, Andy Huang, Nathaniel Albert Trask, Shahed Reza, (2020). Physics-Informed Graph Neural Network for Circuit Compact Model Development International Conference on Semiconductor Simulation of Processes and Devices https://www.osti.gov/search/identifier:1818021 Document ID: 1185071

Paul Allen Kuberry, Nathaniel Albert Trask, Jacob Koester, Pavel B. Bochev, (2020). Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids IMECE International Mechanical Engineering Congress & Exposition Document ID: 1183562

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2020). Robust Training and Initialization of Deep Neural Networks An Adaptive Basis Viewpoint Princeton MSML meeting https://www.osti.gov/search/identifier:1810691 Document ID: 1172850

Mamikon Gulian, Eric Christopher Cyr, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2020). Robust training and initialization of deep neural networks: an adaptive basis viewpoint 2020 Siam-caims An20 https://www.osti.gov/search/identifier:1808257 Document ID: 1161889

Nathaniel Albert Trask, (2020). Physics-informed graph neural nets A unification of NN architectures with mimetic PDE discretization SIAM Annual meeting (virtual) https://www.osti.gov/search/identifier:1808025 Document ID: 1161773

Xujiao Gao, Andy Huang, Nathaniel Albert Trask, Shahed Reza, (2020). Physics-Informed Graph Neural Network for Circuit Compact Model Development Sispad 2020 Document ID: 1140402

Nathaniel Albert Trask, (2020). Physics-informed graph neural nets (pigNNS) A unification of NN architectures with mimetic PDE discretization Tufts data science webinar https://www.osti.gov/search/identifier:1798063 Document ID: 1140330

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mamikon Gulian, Eric Christopher Cyr, (2020). A block coordinate descent optimizer for classification problems exploiting convexity Arxiv https://www.osti.gov/search/identifier:1834091 Document ID: 1140140

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mitchell Wood, Eric Christopher Cyr, (2020). A physics-informed operator regression framework for extracting data-driven continuum models Arxiv https://www.osti.gov/search/identifier:1725869 Document ID: 1138672

Huaiqian You, Yue Yu, Nathaniel Albert Trask, Mamikon Gulian, Marta D’Elia, (2020). Data-driven learning of robust nonlocal physics from high-fidelity synthetic data Arxiv https://www.osti.gov/search/identifier:1765754 Document ID: 1128470

Masoud Behzadinasab, Yuri Bazilevs, Nathaniel Albert Trask, (2020). A unified, higher-order meshfree framework for peridynamic correspondence modeling. Part I: development of a stable formulation in the strong form Arxiv https://www.osti.gov/search/identifier:1668361 Document ID: 1115929

Kenneth Chadwick Sockwell, Kara J. Peterson, Paul Allen Kuberry, Pavel B. Bochev, Nathaniel Albert Trask, (2020). Interface Flux Recovery Coupling Method for the Ocean-Atmosphere System Results in Applied Mathematics https://www.osti.gov/search/identifier:1619234 Document ID: 1115388

Nathaniel Albert Trask, Ravi Ghanshyam Patel, Ben Gross, Paul Atzberger, (2020). GMLS-Nets: A machine learning framework for unstructured data 2020 AAAI SPRING SYMPOSIUM (Virtual meeting) https://www.osti.gov/search/identifier:1773276 Document ID: 1114933

Nathaniel Albert Trask, (2020). Compatible meshfree discretization UIUC Engineering Colloquium https://www.osti.gov/search/identifier:1773275 Document ID: 1091256

Andy Huang, Nathaniel Albert Trask, Xujiao Gao, Shahed Reza, (2020). Physics-Informed, Multi-Stage Machine Learning for Circuit Compact Models SIAM Conference on Mathematics of Data Science (MDS20) Document ID: 1102886

Paul Allen Kuberry, Mauro Perego, Nathaniel Albert Trask, Pavel B. Bochev, (2020). Field reconstruction from Raviart-Thomas, Nedelec, and finite volume degrees-of-freedom using Generalized Moving Least Squares Joint Mathematics Meeting https://www.osti.gov/search/identifier:1761038 Document ID: 1079309

Yu Leng, Xiaochuan Tian, Nathaniel Albert Trask, John Foster, (2020). Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation Computer methods in applied mechanics and engineering https://www.osti.gov/search/identifier:1670723 Document ID: 1078784

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, Denis Ridzal, Stefanie Guenther (LLNL), Lars Ruthotto (Emory), Jacob B. Schroder (UNM), Nico R. Gauger (TU Kaiserslautern), (2019). Improved Neural Network Training: Layer-Parallelism, Least-squares and Initialization International Workshop On Scientific Machine Learning https://www.osti.gov/search/identifier:1643364 Document ID: 1078760

Nathaniel Albert Trask, Ravi Ghanshyam Patel, Ben Gross, Paul Atzberger, (2019). GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data Neural Information Processing Systems https://www.osti.gov/search/identifier:1643425 Document ID: 1067987

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2019). Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint Mathematical and Scientific Machine Learning Conference https://www.osti.gov/search/identifier:1643463 Document ID: 1067715

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, Stefanie (LLNL) Guenther, Lars (Emory University) Ruthotto, Jacob B Schroder, (UNM), Nico R. (TU Kaiserslautern) Gauger, (2019). Improved Neural Network Training: Layer-Parallelism, Least-squares and Initialization International Workshop on Scientific Machine Learning Document ID: 1067481

Nathaniel Albert Trask, (2019). Compatible meshfree discretization Tufts applied math seminar https://www.osti.gov/search/identifier:1646410 Document ID: 1066905

Nathaniel Albert Trask, Andy Huang, (2019). Physics informed machine learning at SNL LANL seminar https://www.osti.gov/search/identifier:1646432 Document ID: 1056618

Kenneth Chadwick Sockwell, Paul Allen Kuberry, Pavel B. Bochev, Nathaniel Albert Trask, Kara J. Peterson, (2019). Bulk-Interface-Flux-Recovery (Bulk-IFR) Method for Coupling the Atmosphere-Ocean Interface Conference on Computational Mathematics and Applications https://www.osti.gov/search/identifier:1642998 Document ID: 1054133

Nathaniel Albert Trask, (2019). Spatially compatible meshfree discretization through GMLS and graph theory Lehigh Math Department Seminar https://www.osti.gov/search/identifier:1675161 Document ID: 1032974

Will Pazner, Nathaniel Albert Trask, Paul Atzberger, (2019). Stochastic Discontinuous Galerkin Methods based on fluctuation-dissipation balance Results in applied mathematics https://www.osti.gov/search/identifier:1574443 Document ID: 1032471

Wei Hu, Nathaniel Albert Trask, Xiaozhe Hu, Wenxiao Pan, (2019). A spatially adaptive high-order meshless method for fluid-structure interactions Cmame https://www.osti.gov/search/identifier:1570255 Document ID: 1031659

Pavel B. Bochev, Peter Andrew Bosler, Paul Allen Kuberry, Mauro Perego, Kara J. Peterson, Nathaniel Albert Trask, (2019). Compatible Particle Discretizations. Final LDRD Report https://www.osti.gov/search/identifier:1569143 Document ID: 1020557

Kenneth Chadwick Sockwell, Kara J. Peterson, Pavel B. Bochev, Paul Allen Kuberry, Nathaniel Albert Trask, (2019). Bulk-Interface-Flux-Recovery (Bulk-IFR) Method for Coupling the Atmosphere-Ocean Interface Conference on Computational Mathematics and Applications (CCMA) Document ID: 1009903

Pavel B. Bochev, Nathaniel Albert Trask, Mauro Perego, (2019). Mimetic meshfree methods or how to be compatible without a mesh 9th International Conference on Numerical Methods for Multi-Material Fluid Flow https://www.osti.gov/search/identifier:1641675 Document ID: 997947

Pavel B. Bochev, Paul Allen Kuberry, Nathaniel Albert Trask, Mauro Perego, (2019). The amazing powers of Generalized Moving Least-Squares Minimum Residual & Least-Squares Finite Element Methods https://www.osti.gov/search/identifier:1641676 Document ID: 997949

Pavel B. Bochev, Nathaniel Albert Trask, Mauro Perego, (2019). A meshfree mimetic divergence operator https://www.osti.gov/search/identifier:1763214 Document ID: 997951

Ravi Ghanshyam Patel, Paul Atzberger, Nathaniel Albert Trask, Eric Christopher Cyr, (2019). Operator Regression for PDE Discovery Sandia Machine Learning and Deep Learning Workshop https://www.osti.gov/search/identifier:1641512 Document ID: 997849

Yu Leng, Xiaochuan Tian, Nathaniel Albert Trask, John Foster, (2019). Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion SIAM journal of numerical analysis https://www.osti.gov/search/identifier:1738919 Document ID: 997281

Pavel B. Bochev, Nathaniel Albert Trask, Paul Allen Kuberry, Mauro Perego, (2019). The amazing powers of Generalized Moving Least-Squares Minimum Residual & Least-Squares Finite Element Methods Document ID: 996745

Ravi Ghanshyam Patel, Paul Atzberger, Nathaniel Albert Trask, Eric Christopher Cyr, (2019). Operator Regression for PDE Discovery Deep Learning for Science School https://www.osti.gov/search/identifier:1641236 Document ID: 986139

Pavel B. Bochev, Kara J. Peterson, Paul Allen Kuberry, Nathaniel Albert Trask, (2019). Non-iterative partitioned methods based on monolithic formulations of the coupled problem 2019 Scientific Discovery through Advanced Compu!ng Principal Investigator (PI) Meeting https://www.osti.gov/search/identifier:1641144 Document ID: 985664

Mauro Perego, Pavel B. Bochev, Paul Allen Kuberry, Nathaniel Albert Trask, (2019). Generalized Moving Least Squares: Approximation Theory and Applications Seminar at Humboldt University, Berlin https://www.osti.gov/search/identifier:1645573 Document ID: 973722

Paul Allen Kuberry, Mauro Perego, Nathaniel Albert Trask, Pavel B. Bochev, (2019). The Compadre Toolkit for Native Degrees-of-Freedom 2019 Scientific Discovery through Advanced Computing Principal Investigator (PI) Meeting https://www.osti.gov/search/identifier:1641034 Document ID: 985090

Mauro Perego, Pavel B. Bochev, Peter Andrew Bosler, Paul Allen Kuberry, Kara J. Peterson, Nathaniel Albert Trask, (2019). Advances in the Approximation Theory of Generalized Moving Least Squares Approximation Theory 16 https://www.osti.gov/search/identifier:1640218 Document ID: 961852

Kara J. Peterson, Pavel B. Bochev, Paul Allen Kuberry, Nathaniel Albert Trask, (2019). Lagrange-Multiplier-Based Partitioned Method for Ocean-Atmosphere Coupling VIII International Conference on Coupled Problems in Science and Engineering https://www.osti.gov/search/identifier:1640221 Document ID: 972627

Paul Allen Kuberry, Mauro Perego, Nathaniel Albert Trask, Pavel B. Bochev, (2019). Field reconstruction from native degrees-of-freedom using the Compadre Toolkit Coupled Problems 2019 https://www.osti.gov/search/identifier:1640167 Document ID: 972343

Ben Gross, Nathaniel Albert Trask, Paul Allen Kuberry, P.J. Atzberger, (2019). Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving Least-Squares (GMLS) Approach. arXiv.org https://www.osti.gov/search/identifier:1619207 Document ID: 972093

Nathaniel Albert Trask, Pavel B. Bochev, Mauro Perego, (2019). Mimetic Conservation Principles for Meshfree Approximation Approximation Theory 16 https://www.osti.gov/search/identifier:1640111 Document ID: 971882

Pavel B. Bochev, Nathaniel Albert Trask, Paul Allen Kuberry, Mauro Perego, (2019). Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems 12th International Conference on Large-Scale Scientific Computations https://www.osti.gov/search/identifier:1640065 Document ID: 961657

Mauro Perego, Pavel B. Bochev, Nathaniel Albert Trask, Peter Andrew Bosler, Paul Allen Kuberry, Kara J. Peterson, (2019). Advances in the Approximation Theory for Generalized Moving Least Squares Finite Element in Fluids https://www.osti.gov/search/identifier:1639699 Document ID: 948336

Nathaniel Albert Trask, (2019). Discrete meshfree conservation principles Fef2019 https://www.osti.gov/search/identifier:1639674 Document ID: 948306

Nathaniel Albert Trask, (2019). Compatible meshfree discretization: Mathematical advances and current projects CEER workshop at UCSD https://www.osti.gov/search/identifier:1644573 Document ID: 937498

Nathaniel Albert Trask, Paul Allen Kuberry, (2019). Compatible meshfree discretization of surface PDE Computational Particle Mechanics (Special issue:Meshfree and Particle Methods for Modeling Extreme Loadings) https://www.osti.gov/search/identifier:1528998 Document ID: 937459

Nathaniel Albert Trask, Pavel B. Bochev, Mauro Perego, (2019). A conservative, consistent, and scalable meshfree mimetic method Journal of Computational Physics https://www.osti.gov/search/identifier:1618096 Document ID: 936556

Pavel B. Bochev, Nathaniel Albert Trask, Paul Allen Kuberry, Mauro Perego, (2019). Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems 12th International Conference on Large-Scale Scientific Computations https://www.osti.gov/search/identifier:1639268 Document ID: 935949

Pavel B. Bochev, Nathaniel Albert Trask, Paul Allen Kuberry, Mauro Perego, (2019). A New Meshfree Variational Approach for PDEs 12th International Conference on Large-Scale Scientific Computations Document ID: 935638

Nathaniel Albert Trask, Pavel B. Bochev, Mauro Perego, (2019). Mimetic conservation principles for meshfree discretization 12th International Conference on Large-Scale Scientific Computations Document ID: 935640

Nathaniel Albert Trask, (2019). Asymptotically compatible foundations for nonlocal mechanics Siam:CSE https://www.osti.gov/search/identifier:1602160 Document ID: 935524

Nathaniel Albert Trask, Benjamin Ashley Huntington, David John Littlewood, (2019). Asymptotically compatible meshfree discretization of state-based peridynamics for linearly elastic composite materials Arxiv preprint Document ID: 935552

Nathaniel Albert Trask, (2019). Spatially compatible meshfree discretization BU Department seminar https://www.osti.gov/search/identifier:1598095 Document ID: 913754

Paul Allen Kuberry, Mauro Perego, Nathaniel Albert Trask, Pavel B. Bochev, (2019). Data Transfer and Coupling of Native Fields with the Compadre Toolkit Coupled Problems 2019 Document ID: 902044

Nathaniel Albert Trask, (2018). Spatially compatible meshfree discretization through GMLS and graph theory RPI mathematics colloquium https://www.osti.gov/search/identifier:1761129 Document ID: 900124

Huaiqian You, Xin Yang Liu, Nathaniel Albert Trask, Yue Yu, (2018). A Neumann-type Boundary Condition For Nonlocal Problems Mathematical Models and Methods in Applied Sciences Document ID: 888963

Nathaniel Albert Trask, Pavel B. Bochev, Mauro Perego, (2018). A consistent and scalable meshfree mimetic method for conservation laws Workshop on Computational Engineering Document ID: 888689

Pavel B. Bochev, Nathaniel Albert Trask, Paul Allen Kuberry, Mauro Perego, Kara J. Peterson, Peter Andrew Bosler, (2018). Compatible meshless methods for DPEs Workshop on Computational Engineering https://www.osti.gov/search/identifier:1806965 Document ID: 877204

Paul Allen Kuberry, Peter Andrew Bosler, Nathaniel Albert Trask, Mauro Perego, Kara J. Peterson, Pavel B. Bochev, (2018). The Compadre Toolkit Nuclear Explosives Code Developer Conference (NECDC) https://www.osti.gov/search/identifier:1594258 Document ID: 876958

Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2018). An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics Computer Methods in Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1474082 Document ID: 853596

Nathaniel Albert Trask, (2018). Discretely conservative meshfree principles for conservation laws USACM meshfree https://www.osti.gov/search/identifier:1592073 Document ID: 854766

Jakob Maljaars, Robert Jan Labeur, Nathaniel Albert Trask, Deborah Sulsky, (2018). Optimization Based Particle-Mesh Algorithm for High-Order and Conservative Scalar Transport Finite Elements Fluid Flow https://www.osti.gov/search/identifier:1575120 Document ID: 842168

Mauro Perego, Pavel B. Bochev, Nathaniel Albert Trask, Peter Andrew Bosler, Paul Allen Kuberry, Kara J. Peterson, (2018). Advances in the Approximation Theory for Functional Reconstructions Using GMLS and Applications to Meshless Discretization of Differential Equations Wccm https://www.osti.gov/search/identifier:1573545 Document ID: 841805

Nathaniel Albert Trask, Mauro Perego, Pavel B. Bochev, (2018). Discretely conservative meshfree schemes for conservation laws World Congress on Computational Mechanics https://www.osti.gov/search/identifier:1806699 Document ID: 841287

Jakob Maljaars, Robert Jan Labeur, Nathaniel Albert Trask, Deborah Sulsky, (2018). Optimization Based Particle-Mesh Algorithm for High-Order and Conservative Scalar Transport Lecture Notes in Computational Science and Engineering Document ID: 830070

Nathaniel Albert Trask, (2018). Spatially compatible meshfree discretization UT:Austin department seminar https://www.osti.gov/search/identifier:1506573 Document ID: 783581

Nathaniel Albert Trask, (2018). Self-force mitigation in unstructured PIC codes using meshfree data transfer WPI department seminar https://www.osti.gov/search/identifier:1504814 Document ID: 783439

Kara J. Peterson, Pavel B. Bochev, Nathaniel Albert Trask, (2018). Improving the Material-Point Method with GMLS UCSD/CEER-Sandia Workshop on Meshfree and Related Computational Methods https://www.osti.gov/search/identifier:1512652 Document ID: 726152

Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2018). A meshfree quadrature rule for nonlocal mechanics Computer Methods in Applied Mechanics and Engineering Document ID: 738213

Mauro Perego, Pavel B. Bochev, Nathaniel Albert Trask, (2017). Approximation Properties of Functional Reconstructions Using GMLS UCSD/CEER-Sandia Workshop on ?Meshfree and Related Computational Methods? Document ID: 726266

Nathaniel Albert Trask, Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2017). Asymptotically compatible meshfree discretization MANNAModeling, Analysis and Numerics for Nonlocal Applications https://www.osti.gov/search/identifier:1512052 Document ID: 737879

Nathaniel Albert Trask, (2017). Consistent and conservative meshfree discretization UCSD/CEER-Sandia Workshop on ?Meshfree and Related Computational Methods? https://www.osti.gov/search/identifier:1512053 Document ID: 726252

Nathaniel Albert Trask, (2017). Compadre: an open-source massive scale meshfree library Localized Kernel-Based Meshless Methods for Partial Differential Equations https://www.osti.gov/search/identifier:1481464 Document ID: 659981

Nathaniel Albert Trask, (2017). Conservative and consistent meshfree method for conservation laws Multimat https://www.osti.gov/search/identifier:1474027 Document ID: 672541

Nathaniel Albert Trask, Pavel B. Bochev, Mauro Perego, (2017). Locally compatible meshless methods for PDEs Multimat 2017 https://www.osti.gov/search/identifier:1471967 Document ID: 672239

Nathaniel Albert Trask, (2017). Particle based methods for the mesoscale Siam:cse https://www.osti.gov/search/identifier:1426395 Document ID: 589440

Nathaniel Albert Trask, (2017). Compatible meshfree discretization with applications to electrophoretic suspension flows Siam:cse https://www.osti.gov/search/identifier:1426394 Document ID: 599471

Nathaniel Albert Trask, (2017). Compatible meshfree discretization with applications to electrophoretic suspension flows Joint math meetings https://www.osti.gov/search/identifier:1416707 Document ID: 566537

Nathaniel Albert Trask, (2016). Meshless methods and continuum simulation CM4 Program Review at Department of Energy https://www.osti.gov/search/identifier:1401943 Document ID: 531806

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