A generalization of the Wiener rational basis functions on infinite intervals: Part I-derivation and properties. - Akil Narayan 001; Jan S. Hesthaven (Math. Comput., 2011)

Sequential data assimilation with multiple models. - Akil Narayan 001; Youssef M. Marzouk; Dongbin Xiu (J. Comput. Phys., 2012)

Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation. - Akil Narayan 001; Dongbin Xiu (SIAM J. Sci. Comput., 2012)

A generalization of the Wiener rational basis functions on infinite intervals, Part II - Numerical investigation. - Akil C. Narayan; Jan S. Hesthaven (J. Comput. Appl. Math., 2013)

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. - John D. Jakeman; Akil Narayan 001; Dongbin Xiu (J. Comput. Phys., 2013)

Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation. - Akil Narayan 001; Dongbin Xiu (SIAM J. Sci. Comput., 2013)

Computational Aspects of Stochastic Collocation with Multifidelity Models. - Xueyu Zhu; Akil Narayan 001; Dongbin Xiu (SIAM/ASA J. Uncertain. Quantification, 2014)

Approximating the Weil-Petersson Metric Geodesics on the Universal Teichmüller Space by Singular Solutions. - Sergey Kushnarev; Akil Narayan 001 (SIAM J. Imaging Sci., 2014)

A Stochastic Collocation Algorithm with Multifidelity Models. - Akil Narayan 001; Claude Jeffrey Gittelson; Dongbin Xiu (SIAM J. Sci. Comput., 2014)

Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation. - Akil Narayan 001; John D. Jakeman (SIAM J. Sci. Comput., 2014)

Multivariate Discrete Least-Squares Approximations with a New Type of Collocation Grid. - Tao Zhou 010; Akil Narayan 001; Zhiqiang Xu (SIAM J. Sci. Comput., 2014)

Weighted discrete least-squares polynomial approximation using randomized quadratures. - Tao Zhou 010; Akil Narayan 001; Dongbin Xiu (J. Comput. Phys., 2015)

A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains. - Yanlai Chen; Sigal Gottlieb; Alfa R. H. Heryudono; Akil Narayan 001 (J. Sci. Comput., 2016)

A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm. - Jiahua Jiang; Yanlai Chen; Akil Narayan 001 (SIAM/ASA J. Uncertain. Quantification, 2016)

Sequential data assimilation with multiple nonlinear models and applications to subsurface flow. - Lun Yang; Akil Narayan 001; Peng Wang 022 (J. Comput. Phys., 2017)

Offline-Enhanced Reduced Basis Method Through Adaptive Construction of the Surrogate Training Set. - Jiahua Jiang; Yanlai Chen; Akil Narayan 001 (J. Sci. Comput., 2017)

Effectively Subsampled Quadratures for Least Squares Polynomial Approximations. - Pranay Seshadri; Akil Narayan 001; Sankaran Mahadevan (SIAM/ASA J. Uncertain. Quantification, 2017)

A Christoffel function weighted least squares algorithm for collocation approximations. - Akil Narayan 001; John D. Jakeman; Tao Zhou 010 (Math. Comput., 2017)

Numerical Computation of Weil-Peterson Geodesics in the Universal Teichmüller Space. - Matt Feiszli; Akil Narayan 001 (SIAM J. Imaging Sci., 2017)

Stochastic Collocation Methods via ℓ1 Minimization Using Randomized Quadratures. - Ling Guo; Akil Narayan 001; Tao Zhou 010; Yuhang Chen (SIAM J. Sci. Comput., 2017)

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions. - John D. Jakeman; Akil Narayan 001; Tao Zhou 010 (SIAM J. Sci. Comput., 2017)

Continuous-Time Stochastic Modeling and Estimation of Electricity Load. - Roohallah Khatami; Masood Parvania; Pramod P. Khargonekar; Akil Narayan 001 (CDC, 2018)

Parametric Topology Optimization with Multi-Resolution Finite Element Models. - Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (CoRR, 2018)

A gradient enhanced ℓ1-minimization for sparse approximation of polynomial chaos expansions. - Ling Guo; Akil Narayan 001; Tao Zhou 010 (J. Comput. Phys., 2018)

Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction. - Jerrad Hampton; Hillary R. Fairbanks; Akil Narayan 001; Alireza Doostan (J. Comput. Phys., 2018)

RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for solving PDEs on surfaces. - Varun Shankar; Akil Narayan 001; Robert M. Kirby (J. Comput. Phys., 2018)

Compressed Sensing with Sparse Corruptions: Fault-Tolerant Sparse Collocation Approximations. - Ben Adcock; Anyi Bao; John D. Jakeman; Akil Narayan 001 (SIAM/ASA J. Uncertain. Quantification, 2018)

Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation. - Ling Guo; Akil Narayan 001; Liang Yan 002; Tao Zhou 010 (SIAM J. Sci. Comput., 2018)

Numerical Integration in Multiple Dimensions with Designed Quadrature. - Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (SIAM J. Sci. Comput., 2018)

A Comparison of Methods for Examining the Effect of Uncertainty in the Conductivities in a Model of Partial Thickness Ischaemia. - Barbara M. Johnston; Akil Narayan 001; Peter R. Johnston (CinC, 2019)

A robust error estimator and a residual-free error indicator for reduced basis methods. - Yanlai Chen; Jiahua Jiang; Akil Narayan 001 (Comput. Math. Appl., 2019)

An efficient solver for cumulative density function-based solutions of uncertain kinematic wave models. - Ming Cheng; Akil Narayan 001; Yi Qin; Peng Wang 022; Xinghui Zhong; Xueyu Zhu (J. Comput. Phys., 2019)

Fast predictive multi-fidelity prediction with models of quantized fidelity levels. - Mani Razi; Robert M. Kirby; Akil Narayan 001 (J. Comput. Phys., 2019)

Data assimilation for models with parametric uncertainty. - Lun Yang; Yi Qin; Akil Narayan 001; Peng Wang 022 (J. Comput. Phys., 2019)

Allocation Strategies for High Fidelity Models in the Multifidelity Regime. - Daniel J. Perry; Robert M. Kirby; Akil Narayan 001; Ross T. Whitaker (SIAM/ASA J. Uncertain. Quantification, 2019)

Convergence Acceleration for Time-Dependent Parametric Multifidelity Models. - Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (SIAM J. Numer. Anal., 2019)

Reduced Basis Methods for Fractional Laplace Equations via Extension. - Harbir Antil; Yanlai Chen; Akil Narayan 001 (SIAM J. Sci. Comput., 2019)

Balanced Truncation for Model Order Reduction of Linear Dynamical Systems with Quadratic Outputs. - Roland Pulch; Akil Narayan 001 (SIAM J. Sci. Comput., 2019)

Using UncertainSCI to Quantify Uncertainty in Cardiac Simulations. - Lindsay C. Rupp; Zexin Liu; Jake A. Bergquist; Sumientra Rampersad; Dan White; Jess D. Tate; Dana H. Brooks; Akil Narayan 001; Rob S. MacLeod (CinC, 2020)

Analysis of The Ratio of $ ell_1$ and $ ell_2$ Norms in Compressed Sensing. - Yiming Xu; Akil Narayan 001; Hoang Tran; Clayton G. Webster (CoRR, 2020)

Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points. - Kyle M. Burk; Akil Narayan 001; Joseph A. Orr (CoRR, 2020)

Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach. - Ling Guo; Akil Narayan 001; Yongle Liu; Tao Zhou 010 (CoRR, 2020)

Generation of nested quadrature rules for generic weight functions via numerical optimization: Application to sparse grids. - Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (J. Comput. Phys., 2020)

Constructing Least-Squares Polynomial Approximations. - Ling Guo; Akil Narayan 001; Tao Zhou 010 (SIAM Rev., 2020)

A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. - Varun Shankar; Grady B. Wright; Akil Narayan 001 (SIAM J. Sci. Comput., 2020)

Structure-Preserving Function Approximation via Convex Optimization. - Vidhi Zala; Mike Kirby; Akil Narayan 001 (SIAM J. Sci. Comput., 2020)

Flexibility Reserve in Power Systems: Definition and Stochastic Multi-Fidelity Optimization. - Roohallah Khatami; Masood Parvania; Akil Narayan 001 (IEEE Trans. Smart Grid, 2020)

Uncertainty Quantification in Simulations of Myocardial Ischemia. - Jake A. Bergquist; Brian Zenger; Lindsay C. Rupp; Akil Narayan 001; Jess D. Tate; Rob S. MacLeod (CinC, 2021)

The Role of Myocardial Fiber Direction in Epicardial Activation Patterns via Uncertainty Quantification. - Lindsay C. Rupp; Jake A. Bergquist; Brian Zenger; Karli Gillette; Akil Narayan 001; Jess D. Tate; Gernot Plank; Rob S. MacLeod (CinC, 2021)

Uncertainty Quantification of the Effects of Segmentation Variability in ECGI. - Jess D. Tate; Wilson W. Good; Nejib Zemzemi; Machteld J. Boonstra; Peter M. van Dam; Dana H. Brooks; Akil Narayan 001; Rob S. MacLeod (FIMH, 2021)

Kernel optimization for Low-Rank Multi-Fidelity Algorithms. - Mani Razi; Robert M. Kirby; Akil Narayan 001 (CoRR, 2021)

Non-Dissipative and Structure-Preserving Emulators via Spherical Optimization. - Dihan Dai; Yekaterina Epshteyn; Akil Narayan 001 (CoRR, 2021)

Physics-Informed Neural Networks (PINNs) for Parameterized PDEs: A Metalearning Approach. - Michael Penwarden; Shandian Zhe; Akil Narayan 001; Robert M. Kirby (CoRR, 2021)

Sensitivity analysis of random linear dynamical systems using quadratic outputs. - Roland Pulch; Akil Narayan 001 (J. Comput. Appl. Math., 2021)

Sensitivity analysis of random linear differential-algebraic equations using system norms. - Roland Pulch; Akil Narayan 001; Tatjana Stykel (J. Comput. Appl. Math., 2021)

Optimal design for kernel interpolation: Applications to uncertainty quantification. - Akil Narayan 001; Liang Yan 002; Tao Zhou 010 (J. Comput. Phys., 2021)

L1-Based Reduced Over Collocation and Hyper Reduction for Steady State and Time-Dependent Nonlinear Equations. - Yanlai Chen; Lijie Ji; Akil Narayan 001; Zhenli Xu (J. Sci. Comput., 2021)

On the Computation of Recurrence Coefficients for Univariate Orthogonal Polynomials. - Zexin Liu; Akil Narayan 001 (J. Sci. Comput., 2021)

Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations. - Dihan Dai; Yekaterina Epshteyn; Akil Narayan 001 (SIAM J. Sci. Comput., 2021)

Multilevel Designed Quadrature for Partial Differential Equations with Random Inputs. - Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (SIAM J. Sci. Comput., 2021)

Structure-Preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods. - Vidhi Zala; Robert M. Kirby; Akil Narayan 001 (SIAM J. Sci. Comput., 2021)

Heart Position Uncertainty Quantification in the Inverse Problem of ECGI. - Jake A. Bergquist; Lindsay C. Rupp; Anna Busatto; Ben Orkild; Brian Zenger; Wilson Good; Jaume Coll-Font; Akil Narayan 001; Jess D. Tate; Dana H. Brooks; Rob S. MacLeod (CinC, 2022)

Effect of Segmentation Uncertainty on the ECGI Inverse Problem Solution and Source Localization. - Narimane Gassa; Machteld J. Boonstra; Beata Ondrusova; Jana Svehlíková; Dana H. Brooks; Akil Narayan 001; Ali S. Rababah; Peter M. van Dam; Rob S. MacLeod; Jess D. Tate; Nejib Zemzemi (CinC, 2022)

Uncertainty Quantification of Cardiac Position on Deep Graph Network ECGI. - Xiajun Jiang; Jess D. Tate; Jake Bergquist; Akil Narayan 001; Rob S. MacLeod; Linwei Wang (CinC, 2022)

The Effect of Segmentation Variability in Forward ECG Simulation. - Beata Ondrusova; Machteld J. Boonstra; Jana Svehlíková; Dana H. Brooks; Peter M. van Dam; Ali S. Rababah; Akil Narayan 001; Rob S. MacLeod; Nejib Zemzemi; Jess D. Tate (CinC, 2022)

Segmentation Uncertainty Quantification in Cardiac Propagation Models. - Jess D. Tate; Nejib Zemzemi; Shireen Y. Elhabian; Beáta Ondrusová; Machteld J. Boonstra; Peter M. van Dam; Akil Narayan 001; Dana H. Brooks; Rob S. MacLeod (CinC, 2022)

Bayesian Continuous-Time Tucker Decomposition. - Shikai Fang; Akil Narayan 001; Robert M. Kirby; Shandian Zhe (ICML, 2022)

Nonparametric Embeddings of Sparse High-Order Interaction Events. - Zheng Wang 042; Yiming Xu; Conor Tillinghast; Shibo Li; Akil Narayan 001; Shandian Zhe (ICML, 2022)

Adaptive density tracking by quadrature for stochastic differential equations. - Ryleigh A. Moore; Akil Narayan 001 (Appl. Math. Comput., 2022)

GP-HMAT: Scalable, O(n log(n)) Gaussian Process Regression with Hierarchical Low-Rank Matrices. - Vahid Keshavarzzadeh; Shandian Zhe; Robert M. Kirby; Akil Narayan 001 (CoRR, 2022)

Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs. - Justin M. Baker; Elena Cherkaev; Akil Narayan 001; Bao Wang 001 (CoRR, 2022)

Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures. - Jarom D. Hogue; Robert M. Kirby; Akil Narayan 001 (CoRR, 2022)

Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs. - Justin M. Baker; Hedi Xia; Yiwei Wang; Elena Cherkaev; Akil Narayan 001; Long Chen; Jack Xin; Andrea L. Bertozzi; Stanley J. Osher; Bao Wang 001 (CoRR, 2022)

Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems. - Osman Asif Malik; Yiming Xu; Nuojin Cheng; Stephen Becker; Alireza Doostan; Akil Narayan 001 (CoRR, 2022)

Quadrature Sampling of Parametric Models with Bi-fidelity Boosting. - Nuojin Cheng; Osman Asif Malik; Yiming Xu; Stephen Becker; Alireza Doostan; Akil Narayan 001 (CoRR, 2022)

Hyperbolicity-preserving and well-balanced stochastic Galerkin method for two-dimensional shallow water equations. - Dihan Dai; Yekaterina Epshteyn; Akil Narayan 001 (J. Comput. Phys., 2022)

Multifidelity modeling for Physics-Informed Neural Networks (PINNs). - Michael Penwarden; Shandian Zhe; Akil Narayan 001; Robert M. Kirby (J. Comput. Phys., 2022)

Fast Barycentric-Based Evaluation Over Spectral/hp Elements. - Edward Laughton; Vidhi Zala; Akil Narayan 001; Robert M. Kirby; David Moxey (J. Sci. Comput., 2022)

Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference. - Elizabeth Qian; Jemima M. Tabeart; Christopher Beattie; Serkan Gugercin; Jiahua Jiang; Peter R. Kramer; Akil Narayan 001 (J. Sci. Comput., 2022)

A Bandit-Learning Approach to Multifidelity Approximation. - Yiming Xu; Vahid Keshavarzzadeh; Robert M. Kirby; Akil Narayan 001 (SIAM J. Sci. Comput., 2022)

Meta-Learning with Adjoint Methods. - Shibo Li; Zheng Wang 042; Akil Narayan 001; Robert M. Kirby; Shandian Zhe (AISTATS, 2023)

Uncertainty Quantification of the Effect of Variable Conductivity in Ventricular Fibrotic Regions on Ventricular Tachycardia. - Jake A. Bergquist; Matthias Lange; Brian Zenger; Benjamin A. Orkild; Eric Paccione; Eugene Kwan; Bram Hunt; Jiawei Dong; Rob S. MacLeod; Akil Narayan 001; Ravi Ranjan (CinC, 2023)

Capturing the Influence of Conduction Velocity on Epicardial Activation Patterns Using Uncertainty Quantification. - Anna Busatto; Lindsay C. Rupp; Karli Gillette; Akil Narayan 001; Gernot Plank; Rob S. MacLeod (CinC, 2023)

A Grid Search of Fibrosis Thresholds for Uncertainty Quantification in Atrial Flutter Simulations. - Benjamin A. Orkild; Jake A. Bergquist; Eric Paccione; Matthias Lange; Eugene Kwan; Bram Hunt; Rob S. MacLeod; Akil Narayan 001; Ravi Ranjan (CinC, 2023)

Uncertainty Quantification of Fiber Orientation and Epicardial Activation. - Lindsay C. Rupp; Anna Busatto; Jake A. Bergquist; Karli Gillette; Akil Narayan 001; Gernot Plank; Rob S. MacLeod (CinC, 2023)

Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks. - Shibo Li; Michael Penwarden; Yiming Xu; Conor Tillinghast; Akil Narayan 001; Mike Kirby; Shandian Zhe (ICML, 2023)

UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering. - Akil Narayan 001; Zexin Liu; Jake A. Bergquist; Chantel Charlebois; Sumientra Rampersad; Lindsay C. Rupp; Dana H. Brooks; Dan White; Jess D. Tate; Rob S. MacLeod (Comput. Biol. Medicine, 2023)

An approximate control variates approach to multifidelity distribution estimation. - Ruijian Han; Akil Narayan 001; Yiming Xu (CoRR, 2023)

Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations. - Dihan Dai; Yekaterina Epshteyn; Akil Narayan 001 (CoRR, 2023)

Budget-limited distribution learning in multifidelity problems. - Yiming Xu; Akil Narayan 001 (Numerische Mathematik, 2023)

Randomized weakly admissible meshes. - Yiming Xu; Akil Narayan 001 (J. Approx. Theory, 2023)

A metalearning approach for Physics-Informed Neural Networks (PINNs): Application to parameterized PDEs. - Michael Penwarden; Shandian Zhe; Akil Narayan 001; Robert M. Kirby (J. Comput. Phys., 2023)

Learning Proper Orthogonal Decomposition of Complex Dynamics Using Heavy-ball Neural ODEs. - Justin M. Baker; Elena Cherkaev; Akil Narayan 001; Bao Wang 001 (J. Sci. Comput., 2023)

A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials. - Zexin Liu; Akil Narayan 001 (SIAM J. Sci. Comput., 2023)

UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines. - Jess D. Tate; Zexin Liu; Jake A. Bergquist; Sumientra Rampersad; Dan White; Chantel Charlebois; Lindsay C. Rupp; Dana H. Brooks; Rob S. MacLeod; Akil Narayan 001 (J. Open Source Softw., 2023)

Convex optimization-based structure-preserving filter for multidimensional finite element simulations. - Vidhi Zala; Akil Narayan 001; Robert M. Kirby (J. Comput. Phys., 2023)

Multi-Resolution Active Learning of Fourier Neural Operators. - Shibo Li; Xin Yu 003; Wei W. Xing; Robert M. Kirby; Akil Narayan 001; Shandian Zhe (AISTATS, 2024)

TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs. - Yanlai Chen; Yajie Ji; Akil Narayan 001; Zhenli Xu (CoRR, 2024)

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning. - Matthew Lowery; John Turnage; Zachary Morrow; John D. Jakeman; Akil Narayan 001; Shandian Zhe; Varun Shankar (CoRR, 2024)

Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation. - Da Long; Zhitong Xu; Guang Yang; Akil Narayan 001; Shandian Zhe (CoRR, 2024)

Energy Stable and Structure-Preserving Algorithms for the Stochastic Galerkin System of 2D Shallow Water Equations. - Yekaterina Epshteyn; Akil Narayan 001; Yinqian Yu (CoRR, 2024)

Subsampling of Parametric Models with Bifidelity Boosting. - Nuojin Cheng; Osman Asif Malik; Yiming Xu; Stephen Becker; Alireza Doostan; Akil Narayan 001 (SIAM/ASA J. Uncertain. Quantification, 2024)

An Approximate Control Variates Approach to Multifidelity Distribution Estimation. - Ruijian Han; Boris Kramer; Dongjin Lee; Akil Narayan 001; Yiming Xu (SIAM/ASA J. Uncertain. Quantification, 2024)

Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods. - Ray Qu; Akil Narayan 001; Jesse Chan (CoRR, 2025)

Hybrid least squares for learning functions from highly noisy data. - Ben Adcock; Bernhard Hientzsch; Akil Narayan 001; Yiming Xu (CoRR, 2025)

Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models. - Ankur; Ram Jiwari; Akil Narayan 001 (J. Sci. Comput., 2025)