Akil Narayan's homepage,

Research Interests

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

Preprints

Title	Author	arXiv / PDF
A Stieltjes algorithm for generating multivariate orthogonal polynomials	Zexin Liu Akil Narayan	arXiv: 2202.04843
Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs	Justin Baker Elena Cherkaev Akil Narayan Bao Wang	arXiv: 2202.12373
GP-HMAT: Scalable, \$\O\(n\textbackslashlog(n))\$ Gaussian Process Regression with Hierarchical Low-Rank Matrices	Vahid Keshavarzzadeh Shandian Zhe Robert M. Kirby Akil Narayan	arXiv: 2201.00888
Physics-Informed Neural Networks (PINNs) for Parameterized PDEs: A Metalearning Approach	Michael Penwarden Shandian Zhe Akil Narayan Robert M. Kirby	arXiv: 2110.13361
Non-Dissipative and Structure-Preserving Emulators via Spherical Optimization	Dihan Dai Yekaterina Epshteyn Akil Narayan	arXiv: 2108.12053
Adaptive Density Tracking by Quadrature for Stochastic Differential Equations	Ryleigh A. Moore Akil Narayan	arXiv: 2105.08148
Budget-limited distribution learning in multifidelity problems	Yiming Xu Akil Narayan	arXiv: 2105.04599
Randomized weakly admissible meshes	Yiming Xu Akil Narayan	arXiv: 2101.04043
Meta-Learning with Adjoint Methods	Shibo Li Zheng Wang Akil Narayan Robert Kirby Shandian Zhe	arXiv: 2110.08432

Published, refereed manuscripts

	Title	Author	Journal			DOI / arXiv
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,	2022	10.3934/mcrf.2021004 arXiv: 1904.09332
74:	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 arXiv:2106.13361
73:	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 arXiv: 2104.11268
72:	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
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 arXiv: 2103.03594
70:	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 (to appear)		2022	arXiv: 2111.13246
69:	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 arXiv: 2106.08316
68:	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
67:	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
66:	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
65:	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
64:	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 arXiv: 2008.08154
63:	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 arXiv: 2009.04812
62:	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 arXiv:2101.01769 [math.NA]
61:	Sensitivity analysis of random linear differential–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
60:	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 arXiv: 2101.11963
59:	Analysis of the ratio of ℓ1 and ℓ2 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 arXiv: 2004.05873
58:	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
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 arXiv: 1808.03707
56:	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 arXiv: 2008.08223
55:	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
54:	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
53:	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
52:	Force-field coefficient optimization of coarse-grained molecular dynamics models with a small computational budget	M. Razi A. Narayan R. M. Kirby D. Bedrov	Computational Materials Science	v176, pp 109518	2020	10.1016/j.commatsci.2020.109518
51:	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
50:	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
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	https://doi.org/10.1002/cnm.3395 arXiv: 2008.04854
48:	Constructing Least-Squares Polynomial Approximations	Ling Guo Akil Narayan Tao Zhou	SIAM Review	v62, pp 483--508	2020	10.1137/18M1234151
47:	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 arXiv: 1812.11601 [math.NA]
46:	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 arXiv:1901.08520 [math.NA]
45:	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 arXiv: 1709.06677 [math.NA]
44:	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 arXiv: 1808.03379
43:	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
42:	Polynomial chaos expansions for dependent random variables	John D. Jakeman Fabian Franzelin Akil Narayan Michael Eldred Dirk Plfüger	Computer Methods in Applied Mechanics and Engineering	v351, pp 643--666	2019	10.1016/j.cma.2019.03.049
41:	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
40:	Sensitivity analysis of random linear dynamical systems using quadratic outputs	Roland Pulch Akil Narayan	Journal of Computational and Applied Mathematics	pp 112491	2019	10.1016/j.cam.2019.112491
39:	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 arXiv:1808.00584 [math.NA]
38:	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 arXiv: 1808.10367 [cs.NA]
37:	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
36:	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
35:	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 arXiv:1708.01296 [math.NA]
34:	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
33:	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 arXiv: 1709.03661
32:	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
31:	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 arXiv:1804.06501 [cs.NA]
30:	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 arXiv:1711.00506 [math]
29:	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 arXiv: 1807.02775
28:	Computation of induced orthogonal polynomial distributions	Akil Narayan	Electronic Transactions on Numerical Analysis	v50, pp 71--97	2018	10.1553/etna_vol50s71 arXiv:1704.08465 [math]
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 arXiv: 1703.00135 [math.NA]
26:	A gradient enhanced ℓ1-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:	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 arXiv: 1412.4305 [math.NA]
24:	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 arXiv:1505.06635 [math.CA]
23:	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 arXiv: 1703.05683 [math]
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 arXiv: 1602.00995 [math.NA]
21:	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 arXiv: 1602.06879 [math.NA]
20:	Numerical Computation of Weil--Peterson Geodesics in the Universal Teichmüller Space	Matt Feiszli Akil Narayan	SIAM Journal on Imaging Sciences	v10, pp 1322--1345	2017	10.1137/15M1043947 arXiv:1307.2358 [math.CV]
19:	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 arXiv: 1601.05470 [math.NA]
18:	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 arXiv: 1707.06394
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 arXiv:1601.00137 [math.NA]
16:	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
15:	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 arXiv:1410.1890 [math]
14:	Stochastic Collocation on Unstructured Multivariate Meshes	Akil Narayan Tao Zhou	Communications in Computational Physics	v18, pp 1--36	2015	10.4208/cicp.020215.070515a arXiv:1501.05891 [math.NA]
13:	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 arXiv:1401.0894 [math.NA]
12:	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
11:	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
10:	Approximating the Weil--Petersson Metric Geodesics on the Universal Teichmüller Space by Singular Solutions	Sergey Kushnarev Akil Narayan	SIAM Journal on Imaging Sciences	v7, pp 900--923	2014	10.1137/120898565 arXiv:1208.2022 [math.CV]
9:	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 arXiv:1404.5663 [math.NA]
8:	A generalization of the Wiener rational basis functions on infinite intervals. Part II — 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
7:	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
6:	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
5:	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
4:	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
3:	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
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–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			DOI / arXiv
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
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
Deterministic Numerical Schemes for the Boltzmann Equation	Akil Narayan Andreas Klöckner			2009	arXiv: 0911.3589