Compact moving least squares: An optimization framework for generating high-order compact meshless discretizations. - Nathaniel Trask; Martin R. Maxey; Xiaozhe Hu (J. Comput. Phys., 2016)

A High-Order Staggered Meshless Method for Elliptic Problems. - Nathaniel Trask; Mauro Perego; Pavel B. Bochev (SIAM J. Sci. Comput., 2017)

A compatible high-order meshless method for the Stokes equations with applications to suspension flows. - Nathaniel Trask; Martin R. Maxey; Xiaozhe Hu (J. Comput. Phys., 2018)

Mesh-Hardened Finite Element Analysis Through a Generalized Moving Least-Squares Approximation of Variational Problems. - Pavel B. Bochev; Nathaniel Trask; Paul Kuberry; Mauro Perego (LSSC, 2019)

Mitigation of the self-force effect in unstructured PIC codes using generalized moving least squares. - Nathaniel Trask; Pavel B. Bochev; Mauro Perego (Comput. Math. Appl., 2019)

Asymptotically compatible meshfree discretization of state-based peridynamics for linearly elastic composite materials. - Nathaniel Trask; Benjamin Huntington; David J. Littlewood (CoRR, 2019)

An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal Problems. - Huaiqian You; Xin Yang Lu; Nathaniel Trask; Yue Yu (CoRR, 2019)

GMLS-Nets: A framework for learning from unstructured data. - Nathaniel Trask; Ravi G. Patel; Ben J. Gross; Paul J. Atzberger (CoRR, 2019)

GMLS-Nets: A Machine Learning Framework for Unstructured Data. - Nathaniel Trask; Ravi G. Patel; Paul J. Atzberger; Ben J. Gross (AAAI Spring Symposium: MLPS, 2020)

Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint. - Eric C. Cyr; Mamikon A. Gulian; Ravi G. Patel; Mauro Perego; Nathaniel A. Trask (MSML, 2020)

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. - Yu Leng; Xiaochuan Tian; Nathaniel A. Trask; John T. Foster (CoRR, 2020)

A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part I: core methods. - Masoud Behzadinasab; Nathaniel Trask; Yuri Bazilevs (CoRR, 2020)

Data-driven learning of robust nonlocal physics from high-fidelity synthetic data. - Huaiqian You; Yue Yu; Nathaniel Trask; Mamikon A. Gulian; Marta D'Elia (CoRR, 2020)

A physics-informed operator regression framework for extracting data-driven continuum models. - Ravi G. Patel; Nathaniel A. Trask; Mitchell A. Wood; Eric C. Cyr (CoRR, 2020)

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach. - Ben J. Gross; Nathaniel Trask; Paul Kuberry; Paul J. Atzberger (J. Comput. Phys., 2020)

A conservative, consistent, and scalable meshfree mimetic method. - Nathaniel Trask; Pavel B. Bochev; Mauro Perego (J. Comput. Phys., 2020)

Greedy Fiedler Spectral Partitioning for Data-driven Discrete Exterior Calculus. - Andy Huang; Nathaniel Trask; Christopher Brissette; Xiaozhe Hu (AAAI Spring Symposium: MLPS, 2021)

Partition of Unity Networks: Deep HP-Approximation. - Kookjin Lee; Nathaniel Trask; Ravi G. Patel; Mamikon A. Gulian; Eric C. Cyr (AAAI Spring Symposium: MLPS, 2021)

A Block Coordinate Descent Optimizer for Classification Problems Exploiting Convexity. - Ravi G. Patel; Nathaniel Trask; Mamikon A. Gulian; Eric C. Cyr (AAAI Spring Symposium: MLPS, 2021)

Machine learning structure preserving brackets for forecasting irreversible processes. - Kookjin Lee; Nathaniel Trask; Panos Stinis (NeurIPS, 2021)

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture. - Yue Yu; Huaiqian You; Nathaniel Trask (CoRR, 2021)

Parallel implementation of a compatible high-order meshless method for the Stokes' equations. - Quang-Thinh Ha; Paul A. Kuberry; Nathaniel A. Trask; Emily M. Ryan (CoRR, 2021)

Probabilistic partition of unity networks: clustering based deep approximation. - Nathaniel Trask; Mamikon A. Gulian; Andy Huang; Kookjin Lee (CoRR, 2021)

A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics. - Masoud Behzadinasab; Mert Alaydin; Nathaniel Trask; Yuri Bazilevs (CoRR, 2021)

Coupling of IGA and Peridynamics for Air-Blast Fluid-Structure Interaction Using an Immersed Approach. - Masoud Behzadinasab; Georgios Moutsanidis; Nathaniel Trask; John T. Foster; Yuri Bazilevs (CoRR, 2021)

Polynomial-Spline Neural Networks with Exact Integrals. - Jonas A. Actor; Andy Huang; Nathaniel Trask (CoRR, 2021)

Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation. - Xinhui Wu; Nathaniel Trask; Jesse Chan (CoRR, 2021)

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion. - Yu Leng; Xiaochuan Tian; Nathaniel Trask; John T. Foster (SIAM J. Numer. Anal., 2021)

Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling. - Kookjin Lee; Nathaniel Trask; Panos Stinis (MSML, 2022)

Hierarchical partition of unity networks: fast multilevel training. - Nathaniel Trask; Amelia Henriksen; Carianne Martinez; Eric C. Cyr (MSML, 2022)

Polynomial-Spline Networks with Exact Integrals and Convergence Rates. - Jonas A. Actor; Andy Huang; Nathaniel Trask (SSCI, 2022)

Efficient optimization-based quadrature for variational discretization of nonlocal problems. - Marco Pasetto; Zhaoxiang Shen; Marta D'Elia; Xiaochuan Tian; Nathaniel Trask; David Kamensky (CoRR, 2022)

Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery. - Nathaniel Trask; Carianne Martinez; Kookjin Lee; Brad Boyce (CoRR, 2022)

Scalable algorithms for physics-informed neural and graph networks. - Khemraj Shukla; Mengjia Xu; Nathaniel Trask; George Em Karniadakis (CoRR, 2022)

Design of experiments for the calibration of history-dependent models via deep reinforcement learning and an enhanced Kalman filter. - Rubén Villarreal; Nikolaos N. Vlassis; Nhon N. Phan; Tommie A. Catanach; Reese E. Jones; Nathaniel A. Trask; Sharlotte L. B. Kramer; WaiChing Sun (CoRR, 2022)

Parameter-varying neural ordinary differential equations with partition-of-unity networks. - Kookjin Lee; Nathaniel Trask (CoRR, 2022)

Probabilistic partition of unity networks for high-dimensional regression problems. - Tiffany Fan; Nathaniel Trask; Marta D'Elia; Eric Darve (CoRR, 2022)

Thermodynamically consistent physics-informed neural networks for hyperbolic systems. - Ravi G. Patel; Indu Manickam; Nathaniel A. Trask; Mitchell A. Wood; Myoungkyu Lee; Ignacio Tomas; Eric C. Cyr (J. Comput. Phys., 2022)

Enforcing exact physics in scientific machine learning: A data-driven exterior calculus on graphs. - Nathaniel Trask; Andy Huang; Xiaozhe Hu (J. Comput. Phys., 2022)

Reversible and irreversible bracket-based dynamics for deep graph neural networks. - Anthony Gruber; Kookjin Lee; Nathaniel Trask (NeurIPS, 2023)

Causal disentanglement of multimodal data. - Elise Walker; Jonas A. Actor; Carianne Martinez; Nathaniel Trask (CoRR, 2023)

A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations. - James H. Adler; Casey Cavanaugh; Xiaozhe Hu; Andy Huang; Nathaniel Trask (SIAM J. Sci. Comput., 2023)

Spiking Physics-Informed Neural Networks on Loihi 2. - Bradley H. Theilman; Qian Zhang; Adar Kahana; Eric C. Cyr; Nathaniel Trask; James B. Aimone; George Em Karniadakis (NICE, 2024)

Graph Convolutions Enrich the Self-Attention in Transformers! - Jeongwhan Choi 002; Hyowon Wi; Jayoung Kim 002; Yehjin Shin; Kookjin Lee; Nathaniel Trask; Noseong Park (NeurIPS, 2024)

A Structure-Preserving Domain Decomposition Method for Data-Driven Modeling. - Shuai Jiang; Jonas A. Actor; Scott A. Roberts; Nathaniel Trask (CoRR, 2024)

Gaussian Variational Schemes on Bounded and Unbounded Domains. - Jonas A. Actor; Anthony Gruber; Eric C. Cyr; Nathaniel Trask (CoRR, 2024)

Data-driven Whitney forms for structure-preserving control volume analysis. - Jonas A. Actor; Xiaozhe Hu; Andy Huang; Scott A. Roberts; Nathaniel Trask (J. Comput. Phys., 2024)

Efficiently Parameterized Neural Metriplectic Systems. - Anthony Gruber; Kookjin Lee; Haksoo Lim; Noseong Park; Nathaniel Trask (ICLR, 2025)

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs. - Adrienne M. Propp; Jonas A. Actor; Elise Walker; Houman Owhadi; Nathaniel Trask; Daniel M. Tartakovsky (CoRR, 2025)

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids. - Paul Kuberry; Pavel B. Bochev; Jacob Koester; Nathaniel Trask (Eng. Comput., 2025)

Structure-Preserving Digital Twins via Conditional Neural Whitney Forms. - Brooks Kinch; Benjamin Shaffer; Elizabeth Armstrong; Michael Meehan; John Hewson; Nathaniel Trask (CoRR, 2025)