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