Akil Narayan, Publications

Research Interests

My research interests lie in numerical analysis, scientific computing, and approximation algorithms.

Publications:

Preprints | Conference Proceedings | Journal Publications

Preprints

Title	Author		arXiv / PDF
Multi-Resolution Active Learning of Fourier Neural Operators	Shibo Li Xin Yu Wei Xing Mike Kirby Akil Narayan Shandian Zhe
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations	Dihan Dai Yekaterina Epshteyn Akil Narayan
An Approximate Control Variates Approach to Multifidelity Distribution Estimation	Ruijian Han Boris Kramer Dongjin Lee Akil Narayan Yiming Xu
Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems	Osman Asif Malik Yiming Xu Nuojin Cheng Stephen Becker Alireza Doostan Akil Narayan
Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures	Jarom D. Hogue Robert M. Kirby Akil Narayan
Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs	Justin Baker Hedi Xia Yiwei Wang Elena Cherkaev Akil Narayan Long Chen Jack Xin Andrea L. Bertozzi Stanley J. Osher Bao Wang
Quadrature Sampling of Parametric Models with Bi-fidelity Boosting	Nuojin Cheng Osman Asif Malik Yiming Xu Stephen Becker Alireza Doostan Akil Narayan
GP-HMAT: Scalable, \$O(N\textbackslash log(n))\$ Gaussian Process Regression with Hierarchical Low-Rank Matrices	Vahid Keshavarzzadeh Shandian Zhe Robert M. Kirby Akil Narayan

Conference Proceedings

	Title	Author	Journal			DOI / arXiv
15:	Largest Angle Path Distance for Multi-Manifold Clustering	Haoyu Chen Anna Little Akil Narayan	Fourteenth International Conference on Sampling Theory and Applications		2023
14:	Largest Angle Path Distance for Multi-Manifold Clustering	Haoyu Chen Anna Little Akil Narayan	2023 International Conference on Sampling Theory and Applications (SampTA)	pp 1--7	2023	10.1109/SampTA59647.2023.10301401
13:	Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks	Shibo Li Michael Penwarden Yiming Xu Conor Tillinghast Akil Narayan Mike Kirby Shandian Zhe	Proceedings of the 40th International Conference on Machine Learning	pp 19855--19881	2023
12:	Meta-Learning with Adjoint Methods	Shibo Li Zheng Wang Akil Narayan Robert Kirby Shandian Zhe	Proceedings of the 26th International Conference on Artificial Intelligence and Statistics	pp 7239--7251	2023
11:	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 Jess Tate Dana Brooks	Computing in Cardiology 2022	pp 1--4	2022	10.22489/CinC.2022.374
10:	Bayesian Continuous-Time Tucker Decomposition	Shikai Fang Akil Narayan Robert Kirby Shandian Zhe	Proceedings of the 39th International Conference on Machine Learning	pp 6235--6245	2022
9:	Uncertainty Quantification of Cardiac Position on Deep Graph Network ECGI	Xiajun Jiang Jess Tate Jake Bergquist Akil Narayan Rob MacLeod Linwei Wang	Computing in Cardiology 2022		2022	10.22489/CinC.2022.425
8:	Nonparametric Embeddings of Sparse High-Order Interaction Events	Zheng Wang Yiming Xu Conor Tillinghast Shibo Li Akil Narayan Shandian Zhe	Proceedings of the 39th International Conference on Machine Learning	pp 23237--23253	2022
7:	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 Jess D Tate Gernot Plank Rob S MacLeod	2021 Computing in Cardiology (CinC)	pp 1--4	2021	10.23919/CinC53138.2021.9662950
6:	Uncertainty Quantification in Simulations of Myocardial Ischemia	Jake A Bergquist Brian Zenger Lindsay C Rupp Akil Narayan Jess Tate Rob S MacLeod	2021 Computing in Cardiology (CinC)	pp 1--4	2021	10.23919/CinC53138.2021.9662837
5:	Uncertainty Quantification of the Effects of Segmentation Variability in ECGI	Jess D. Tate Wilson W. Good Nejib Zemzemi Machteld Boonstra Peter {van Dam} Dana H. Brooks Akil Narayan Rob S. MacLeod	Functional Imaging and Modeling of the Heart	pp 515--522	2021	10.1007/978-3-030-78710-3_49
4:	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 Rob S MacLeod	2020 Computing in Cardiology	pp 1--4	2020	10.22489/CinC.2020.275
3:	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 Peter R Johnston	2019 Computing in Cardiology (CinC)	pp Page 1-Page 4	2019	10.23919/CinC49843.2019.9005728
2:	Continuous-Time Stochastic Modeling and Estimation of Electricity Load	Roohallah Khatami Masood Parvania Pramod Khargonekar Akil Narayan	2018 IEEE Conference on Decision and Control (CDC)	pp 3988--3993	2018	10.1109/CDC.2018.8619042
1:	Sampling High Dimensional Optimal Measures	Akil Narayan	11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013	pp 902--905	2013	10.1063/1.4825644

Journal publications

	Title	Author	Journal			DOI / arXiv
85:	A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs	Michael Penwarden Shandian Zhe Akil Narayan Robert M. Kirby	Journal of Computational Physics	v477, pp 111912	2023	10.1016/j.jcp.2023.111912
84:	A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials	Zexin Liu Akil Narayan	SIAM Journal on Scientific Computing	v45, pp A1125-A1147	2023	10.1137/22M1477131
83:	Convex Optimization-Based Structure-Preserving Filter for Multidimensional Finite Element Simulations	Vidhi Zala Akil Narayan Robert M. Kirby	Journal of Computational Physics	v492, pp 112364	2023	10.1016/j.jcp.2023.112364
82:	Randomized Weakly Admissible Meshes	Yiming Xu Akil Narayan	Journal of Approximation Theory	v285, pp 105835	2023	10.1016/j.jat.2022.105835
81:	Budget-Limited Distribution Learning in Multifidelity Problems	Yiming Xu Akil Narayan	Numerische Mathematik	v153, pp 171--212	2023	10.1007/s00211-022-01337-5
80:	UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines	Jess Tate Zexin Liu Jake A. Bergquist Sumientra Rampersad Dan White Chantel Charlebois Lindsay Rupp Dana H. Brooks Rob S. MacLeod Akil Narayan	Journal of Open Source Software	v8, pp 4249	2023	10.21105/joss.04249
79:	Uncertainty Quantification of the Effect of Cardiac Position Variability in the Inverse Problem of Electrocardiographic Imaging	Jake Aaron Bergquist Brian Zenger Lindsay Rupp Anna Busatto Jess D Tate Dana H Brooks Akil Narayan Rob MacLeod	Physiological Measurement		2023	10.1088/1361-6579/acfc32
78:	Learning Proper Orthogonal Decomposition of Complex Dynamics Using Heavy-ball Neural ODEs	Justin Baker Elena Cherkaev Akil Narayan Bao Wang	Journal of Scientific Computing	v95, pp 54	2023	10.1007/s10915-023-02176-8
77:	UncertainSCI: Uncertainty Quantification for Computational Models in Biomedicine and Bioengineering	Akil Narayan Zexin Liu Jake A. Bergquist Chantel Charlebois Sumientra Rampersad Lindsay Rupp Dana Brooks Dan White Jess Tate Rob S. MacLeod	Computers in Biology and Medicine	v152, pp 106407	2023	10.1016/j.compbiomed.2022.106407
76:	Non-Dissipative and Structure-Preserving Emulators via Spherical Optimization	Dihan Dai Yekaterina Epshteyn Akil Narayan	Information and Inference: A Journal of the IMA	pp iaac021	2022	10.1093/imaiai/iaac021
75:	Model Reduction for Fractional Elliptic Problems Using Kato's Formula	Huy Dinh Harbir Antil Yanlai Chen Elena Cherkaev Akil Narayan	Mathematical Control & Related Fields	v12, pp 115--146	2022	10.3934/mcrf.2021004
74:	Variational Inference for Nonlinear Inverse Problems via Neural Net Kernels: Comparison to Bayesian Neural Networks, Application to Topology Optimization	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	Computer Methods in Applied Mechanics and Engineering	v400, pp 115495	2022	10.1016/j.cma.2022.115495
73:	Uncertainty Quantification for Ecological Models with Random Parameters	Jody R. Reimer Frederick R. Adler Kenneth M. Golden Akil Narayan	Ecology Letters	v25, pp 2232--2244	2022	10.1111/ele.14095
72:	Adaptive Density Tracking by Quadrature for Stochastic Differential Equations	Ryleigh A. Moore Akil Narayan	Applied Mathematics and Computation	v431, pp 127298	2022	10.1016/j.amc.2022.127298
71:	Fast Barycentric-Based Evaluation Over Spectral/Hp Elements	Edward Laughton Vidhi Zala Akil Narayan Robert M. Kirby David Moxey	Journal of Scientific Computing	v90, pp 78	2022	10.1007/s10915-021-01750-2
70:	Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)	Michael Penwarden Shandian Zhe Akil Narayan Robert M. Kirby	Journal of Computational Physics	v451, pp 110844	2022	10.1016/j.jcp.2021.110844
69:	A Bandit-Learning Approach to Multifidelity Approximation	Yiming Xu Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	SIAM Journal on Scientific Computing	v44, pp A150-A175	2022	10.1137/21M1408312
68:	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	Journal of Scientific Computing	v91, pp 29	2022	10.1007/s10915-022-01798-8
67:	Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations	Dihan Dai Yekaterina Epshteyn Akil Narayan	Journal of Computational Physics	v452, pp 110901	2022	10.1016/j.jcp.2021.110901
66:	Structure-Preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/Hp Element Methods	Vidhi Zala Robert M. Kirby Akil Narayan	SIAM Journal on Scientific Computing	v43, pp A3713-A3732	2021	10.1137/20M1337223
65:	Analysis of the Ratio of \$\textbackslash ell\_1\$ and \$\textbackslash ell\_2\$ Norms in Compressed Sensing	Yiming Xu Akil Narayan Hoang Tran Clayton G. Webster	Applied and Computational Harmonic Analysis	v55, pp 486--511	2021	10.1016/j.acha.2021.06.006
64:	Kernel Optimization for Low-Rank Multifidelity Algorithms	Mani Razi Robert Mike Kirby Akil Narayan	International Journal for Uncertainty Quantification	v11, pp 31--54	2021	10.1615/Int.J.UncertaintyQuantification.2020033212
63:	Sensitivity Analysis of Random Linear Differential\textendash Algebraic Equations Using System Norms	Roland Pulch Akil Narayan Tatjana Stykel	Journal of Computational and Applied Mathematics	v397, pp 113666	2021	10.1016/j.cam.2021.113666
62:	On the Computation of Recurrence Coefficients for Univariate Orthogonal Polynomials	Zexin Liu Akil Narayan	Journal of Scientific Computing	v88, pp 53	2021	10.1007/s10915-021-01586-w
61:	Robust Topology Optimization with Low Rank Approximation Using Artificial Neural Networks	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	Computational Mechanics	v68, pp 1297--1323	2021	10.1007/s00466-021-02069-3
60:	Multilevel Designed Quadrature for Partial Differential Equations with Random Inputs	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	SIAM Journal on Scientific Computing	v43, pp A1412-A1440	2021	10.1137/20M1333407
59:	Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations	Dihan Dai Yekaterina Epshteyn Akil Narayan	SIAM Journal on Scientific Computing	v43, pp A929-A952	2021	10.1137/20M1360736
58:	L1-Based Reduced Over Collocation and Hyper Reduction for Steady State and Time-Dependent Nonlinear Equations	Yanlai Chen Lijie Ji Akil Narayan Zhenli Xu	Journal of Scientific Computing	v87, pp 10	2021	10.1007/s10915-021-01416-z
57:	Generation of Nested Quadrature Rules for Generic Weight Functions via Numerical Optimization: Application to Sparse Grids	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	Journal of Computational Physics	v400, pp 108979	2020	10.1016/j.jcp.2019.108979
56:	Sparse Approximation of Data-Driven Polynomial Chaos Expansions: An Induced Sampling Approach	Ling Guo Akil Narayan Yongle Liu Tao Zhou	Communications in Mathematical Research	v36, pp 128--153	2020	10.4208/cmr.2020-0010
55:	Flexibility Reserve in Power Systems: Definition and Stochastic Multi-Fidelity Optimization	Roohallah Khatami Masood Parvania Akil Narayan	IEEE Transactions on Smart Grid	v11, pp 644--654	2020	10.1109/TSG.2019.2927600
54:	Optimal Design for Kernel Interpolation: Applications to Uncertainty Quantification	Akil Narayan Liang Yan Tao Zhou	Journal of Computational Physics	v430, pp 110094	2020	10.1016/j.jcp.2020.110094
53:	Force-Field Coefficient Optimization of Coarse-Grained Molecular Dynamics Models with a Small Computational Budget	Mani Razi Akil Narayan Robert M. Kirby Dmitry Bedrov	Computational Materials Science	v176, pp 109518	2020	10.1016/j.commatsci.2020.109518
52:	Stress-Based Topology Optimization under Uncertainty via Simulation-Based Gaussian Process	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	Computer Methods in Applied Mechanics and Engineering	v365, pp 112992	2020	10.1016/j.cma.2020.112992
51:	Structure-Preserving Function Approximation via Convex Optimization	Vidhi Zala Mike Kirby Akil Narayan	SIAM Journal on Scientific Computing	v42, pp A3006-A3029	2020	10.1137/19M130128X
50:	Constructing Least-Squares Polynomial Approximations	Ling Guo Akil Narayan Tao Zhou	SIAM Review	v62, pp 483--508	2020	10.1137/18M1234151
49:	Efficient Sampling for Polynomial Chaos-Based Uncertainty Quantification and Sensitivity Analysis Using Weighted Approximate Fekete Points	Kyle M. Burk Akil Narayan Joseph A. Orr	International Journal for Numerical Methods in Biomedical Engineering	v36, pp e3395	2020	10.1002/cnm.3395
48:	An Efficient Method of Calculating Composition-Dependent Inter-Diffusion Coefficients Based on Compressed Sensing Method	Yi Qin Akil Narayan Kaiming Cheng Peng Wang	Computational Materials Science	v188, pp 110145	2020	10.1016/j.commatsci.2020.110145
47:	A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds	Varun Shankar Grady B. Wright Akil Narayan	SIAM Journal on Scientific Computing	v42, pp A2371-A2401	2020	10.1137/19M1288747
46:	Convergence Acceleration for Time-Dependent Parametric Multifidelity Models	V. Keshavarzzadeh R. Kirby A. Narayan	SIAM Journal on Numerical Analysis	v57, pp 1344--1368	2019	10.1137/18M1170339
45:	Polynomial Chaos Expansions for Dependent Random Variables	John D. Jakeman Fabian Franzelin Akil Narayan Michael Eldred Dirk Plf{\"u}ger	Computer Methods in Applied Mechanics and Engineering	v351, pp 643--666	2019	10.1016/j.cma.2019.03.049
44:	Data Assimilation for Models with Parametric Uncertainty	Lun Yang Yi Qin Akil Narayan Peng Wang	Journal of Computational Physics	v396, pp 785--798	2019	10.1016/j.jcp.2019.07.020
43:	A Robust Error Estimator and a Residual-Free Error Indicator for Reduced Basis Methods	Yanlai Chen Jiahua Jiang Akil Narayan	Computers & Mathematics with Applications	v77, pp 1963--1979	2019	10.1016/j.camwa.2018.11.032
42:	An Efficient Solver for Cumulative Density Function-Based Solutions of Uncertain Kinematic Wave Models	Ming Cheng Akil Narayan Yi Qin Peng Wang Xinghui Zhong Xueyu Zhu	Journal of Computational Physics	v382, pp 138--151	2019	10.1016/j.jcp.2019.01.008
41:	Allocation Strategies for High Fidelity Models in the Multifidelity Regime	Daniel J. Perry Robert M. Kirby Akil Narayan Ross T. Whitaker	SIAM/ASA Journal on Uncertainty Quantification	v7, pp 203--231	2019	10.1137/17M1144714
40:	Balanced Truncation for Model Order Reduction of Linear Dynamical Systems with Quadratic Outputs	Roland Pulch Akil Narayan	SIAM Journal on Scientific Computing	v41, pp A2270-A2295	2019	10.1137/17M1148797
39:	An Error Bound for the Standard Deviation in Model Order Reduction of Linear Stochastic Galerkin Systems	Roland Pulch Akil Narayan	Proceedings in Applied Mathematics and Mechanics	v19, pp e201900028	2019	10.1002/pamm.201900028
38:	Sensitivity Analysis of Random Linear Dynamical Systems Using Quadratic Outputs	Roland Pulch Akil Narayan	Journal of Computational and Applied Mathematics	v387, pp 112491	2019	10.1016/j.cam.2019.112491
37:	Parametric Topology Optimization with Multiresolution Finite Element Models	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	International Journal for Numerical Methods in Engineering	v119, pp 567--589	2019	10.1002/nme.6063
36:	Fast Predictive Multi-Fidelity Prediction with Models of Quantized Fidelity Levels	Mani Razi Robert M. Kirby Akil Narayan	Journal of Computational Physics	v376, pp 992--1008	2019	10.1016/j.jcp.2018.10.025
35:	Reduced Basis Methods for Fractional Laplace Equations via Extension	Harbir Antil Yanlai Chen Akil Narayan	SIAM Journal on Scientific Computing	v41, pp A3552-A3575	2019	10.1137/18M1204802
34:	Computation of induced orthogonal polynomial distributions	Akil Narayan	Electronic Transactions on Numerical Analysis	v50, pp 71--97	2018	10.1553/etna_vol50s71
33:	Numerical Integration in Multiple Dimensions with Designed Quadrature	Vahid Keshavarzzadeh Robert M. Kirby Akil Narayan	SIAM Journal on Scientific Computing	v40, pp A2033-A2061	2018	10.1137/17M1137875
32:	Generation and Application of Multivariate Polynomial Quadrature Rules	John D. Jakeman Akil Narayan	Computer Methods in Applied Mechanics and Engineering	v338, pp 134--161	2018	10.1016/j.cma.2018.04.009
31:	Fast Predictive Models Based on Multi-Fidelity Sampling of Properties in Molecular Dynamics Simulations	Mani Razi Akil Narayan Robert M. Kirby Dmitry Bedrov	Computational Materials Science	v152, pp 125--133	2018	10.1016/j.commatsci.2018.05.029
30:	Practical Error Bounds for a Non-Intrusive Bi-Fidelity Approach to Parametric/Stochastic Model Reduction	Jerrad Hampton Hillary R. Fairbanks Akil Narayan Alireza Doostan	Journal of Computational Physics	v368, pp 315--332	2018	10.1016/j.jcp.2018.04.015
29:	Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation	Ling Guo Akil Narayan Liang Yan Tao Zhou	SIAM Journal on Scientific Computing	v40, pp A366-A387	2018	10.1137/17M1140960
28:	RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces	Varun Shankar Akil Narayan Robert M. Kirby	Journal of Computational Physics	v373, pp 722--735	2018	10.1016/j.jcp.2018.07.015
27:	Compressed Sensing with Sparse Corruptions: Fault-Tolerant Sparse Collocation Approximations	Ben Adcock Anyi Bao John D. Jakeman Akil Narayan	SIAM/ASA Journal on Uncertainty Quantification	v6, pp 1424--1453	2018	10.1137/17M112590X
26:	A Gradient Enhanced \$\textbackslash ell\_1\$-Minimization for Sparse Approximation of Polynomial Chaos Expansions	Ling Guo Akil Narayan Tao Zhou	Journal of Computational Physics	v367, pp 49--64	2018	10.1016/j.jcp.2018.04.026
25:	Effectively Subsampled Quadratures for Least Squares Polynomial Approximations	Pranay Seshadri Akil Narayan Sankaran Mahadevan	SIAM/ASA Journal on Uncertainty Quantification	v5, pp 1003--1023	2017	10.1137/16M1057668
24:	A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions	John Jakeman Akil Narayan Tao Zhou	SIAM Journal on Scientific Computing	v39, pp A1114-A1144	2017	10.1137/16M1063885
23:	A Christoffel Function Weighted Least Squares Algorithm for Collocation Approximations	Akil Narayan John Jakeman Tao Zhou	Mathematics of Computation	v86, pp 1913--1947	2017	10.1090/mcom/3192
22:	Stochastic Collocation Methods via L1 Minimization Using Randomized Quadratures	Ling Guo Akil Narayan Tao Zhou Yuhang Chen	SIAM Journal on Scientific Computing	v39, pp A333-A359	2017	10.1137/16M1059680
21:	Offline-Enhanced Reduced Basis Method Through Adaptive Construction of the Surrogate Training Set	Jiahua Jiang Yanlai Chen Akil Narayan	Journal of Scientific Computing	v73, pp 853--875	2017	10.1007/s10915-017-0551-3
20:	Sequential Data Assimilation with Multiple Nonlinear Models and Applications to Subsurface Flow	Lun Yang Akil Narayan Peng Wang	Journal of Computational Physics	v346, pp 356--368	2017	10.1016/j.jcp.2017.06.026
19:	Numerical Computation of Weil--Peterson Geodesics in the Universal Teichm\"uller Space	Matt Feiszli Akil Narayan	SIAM Journal on Imaging Sciences	v10, pp 1322--1345	2017	10.1137/15M1043947
18:	An Orthogonality Property of the Legendre Polynomials	Len Bos Akil Narayan Norman Levenberg Federico Piazzon	Constructive Approximation	v45, pp 65--81	2017	10.1007/s00365-015-9321-3
17:	A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm	Jiang Jiang Yanlai Chen Akil Narayan	SIAM/ASA Journal on Uncertainty Quantification	v4, pp 1398--1420	2016	10.1137/16M1055736
16:	A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains	Yanlai Chen Sigal Gottlieb Alfa Heryudono Akil Narayan	Journal of Scientific Computing	v66, pp 67--90	2015	10.1007/s10915-015-0013-8
15:	Stochastic Collocation on Unstructured Multivariate Meshes	Akil Narayan Tao Zhou	Communications in Computational Physics	v18, pp 1--36	2015	10.4208/cicp.020215.070515a
14:	Weighted Discrete Least-Squares Polynomial Approximation Using Randomized Quadratures	Tao Zhou Akil Narayan Dongbin Xiu	Journal of Computational Physics	v298, pp 787--800	2015	10.1016/j.jcp.2015.06.042
13:	Approximating the Weil--Petersson Metric Geodesics on the Universal Teichm\"uller Space by Singular Solutions	Sergey Kushnarev Akil Narayan	SIAM Journal on Imaging Sciences	v7, pp 900--923	2014	10.1137/120898565
12:	A Stochastic Collocation Algorithm with Multifidelity Models	Akil Narayan Claude Gittelson Dongbin Xiu	SIAM Journal on Scientific Computing	v36, pp A495-A521	2014	10.1137/130929461
11:	Computational Aspects of Stochastic Collocation with Multifidelity Models	Xueyu Zhu Akil Narayan Dongbin Xiu	SIAM/ASA Journal on Uncertainty Quantification	v2, pp 444--463	2014	10.1137/130949154
10:	Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation	Akil Narayan John Jakeman	SIAM Journal on Scientific Computing	v36, pp A2952-A2983	2014	10.1137/140966368
9:	Multivariate Discrete Least-Squares Approximations with a New Type of Collocation Grid	Tao Zhou Akil Narayan Zhiqiang Xu	SIAM Journal on Scientific Computing	v36, pp A2401-A2422	2014	10.1137/130950434
8:	Minimal Multi-Element Stochastic Collocation for Uncertainty Quantification of Discontinuous Functions	John D. Jakeman Akil Narayan Dongbin Xiu	Journal of Computational Physics	v242, pp 790--808	2013	10.1016/j.jcp.2013.02.035
7:	Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation	Akil Narayan Dongbin Xiu	SIAM Journal on Scientific Computing	v35, pp A2293-A2315	2013	10.1137/12089613X
6:	A Generalization of the Wiener Rational Basis Functions on Infinite Intervals. Part II \textemdash Numerical Investigation	Akil C. Narayan Jan S. Hesthaven	Journal of Computational and Applied Mathematics	v237, pp 18--34	2013	10.1016/j.cam.2012.06.036
5:	Computation of Connection Coefficients and Measure Modifications for Orthogonal Polynomials	Akil Narayan Jan Hesthaven	BIT Numerical Mathematics	v52, pp 457--483	2012	10.1007/s10543-011-0363-z
4:	Sequential Data Assimilation with Multiple Models	Akil Narayan Youssef Marzouk Dongbin Xiu	Journal of Computational Physics	v231, pp 6401--6418	2012	10.1016/j.jcp.2012.06.002
3:	Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation	Akil Narayan Dongbin Xiu	SIAM Journal on Scientific Computing	v34, pp A1729-A1752	2012	10.1137/110854059
2:	Distributional Sensitivity for Uncertainty Quantification	Akil Narayan Dongbin Xiu	Communications in Computational Physics	v10, pp 140--160	2011	10.4208/cicp.160210.300710a
1:	A Generalization of the Wiener Rational Basis Functions on Infinite Intervals: Part I\textendash Derivation and Properties	Akil C. Narayan Jan S. Hesthaven	Mathematics of Computation	v80, pp 1557--1583	2011	10.1090/S0025-5718-2010-02437-8

Unrefereed proceedings and reports

Title	Author	Journal
Postdoctoral Needs and Concerns: Purdue University and Beyond	Akil Narayan Nicole Weber Peter Richtsmeier Valentina Trinetta David Nelson	The POSTDOCket	v10, pp 5--6	2012
A Generalization of the Wiener Rational Basis Functions on Infinite Intervals	Akil Narayan	PhD Thesis, Brown University		2009
Deterministic Numerical Schemes for the Boltzmann Equation	Akil Narayan Andreas Kl{\"o}ckner			2009