Research Interests


Broadly speaking, my research interests are numerical analysis, scientific computing, and approximation algorithms.



Published and submitted papers are listed below.

Submitted


Title Author arXiv / PDF
Model reduction for fractional elliptic problems using Kato's formula Huy Dinh
Harbir Antil
Yanlai Chen
Elena Cherkaev
Akil Narayan
arXiv: 1904.09332
Generation of Nested Quadrature Rules for Generic Weight Functions via Numerical Optimization: Application to Sparse Grids Vahid Keshavarzzadeh
Robert M. Kirby
Akil Narayan
arXiv: 1808.03707
Certified reduced basis methods for fractional Laplace equations via extension Harbir Antil
Yanlai Chen
Akil Narayan
arXiv: 1808.00584


Published


Title Author Journal DOI / arXiv
Flexibility Reserve in Power Systems: Definition and Stochastic Multi-Fidelity Optimization R. Khatami
M. Parvania
A. Narayan
IEEE Transactions on Smart Grid
pp 1--1 (2019)
10.1109/TSG.2019.2927600
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)
https://doi.org/10.1016/j.jcp.2018.10.025
Balanced Truncation for Model Order Reduction of Linear Dynamical Systems with Quadratic Outputs R. Pulch
A. Narayan
SIAM Journal on Scientific Computing
pp A2270--A2295 (2019)
10.1137/17M1148797
arXiv: 1709.06677 [math.NA]
Data assimilation for models with parametric uncertainty Lun Yang
Yi Qin
Akil Narayan
Peng Wang
Journal of Computational Physics
(2019)
10.1016/j.jcp.2019.07.020
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]
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
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]
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
Allocation Strategies for High Fidelity Models in the Multifidelity Regime D. Perry
R. Kirby
A. Narayan
R. Whitaker
SIAM/ASA Journal on Uncertainty Quantification
v7, pp 203--231 (2019)
10.1137/17M1144714
arXiv: 1812.11601 [math.NA]
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
Compressed Sensing with Sparse Corruptions: Fault-Tolerant Sparse Collocation Approximations B. Adcock
A. Bao
J. Jakeman
A. Narayan
SIAM/ASA Journal on Uncertainty Quantification
v6, pp 1424--1453 (2018)
10.1137/17M112590X
arXiv: 1703.00135 [math.NA]
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]
Continuous-Time Stochastic Modeling and Estimation of Electricity Load R. Khatami
M. Parvania
P. Khargonekar
A. Narayan
2018 IEEE Conference on Decision and Control (CDC)
pp 3988--3993
10.1109/CDC.2018.8619042
Numerical Integration in Multiple Dimensions with Designed Quadrature V. Keshavarzzadeh
R. Kirby
A. Narayan
SIAM Journal on Scientific Computing
v40, pp A2033--A2061 (2018)
10.1137/17M1137875
arXiv:1804.06501 [cs.NA]
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
Fast predictive models based on multi-fidelity sampling of properties in molecular dynamics simulations M. Razi
A. Narayan
R. M. Kirby
D. Bedrov
Computational Materials Science
v152, pp 125--133 (2018)
10.1016/j.commatsci.2018.05.029
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]
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
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
Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation L. Guo
A. Narayan
L. Yan
T. Zhou
SIAM Journal on Scientific Computing
v40, pp A366--A387 (2018)
10.1137/17M1140960
arXiv:1708.01296 [math.NA]
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]
Effectively Subsampled Quadratures for Least Squares Polynomial Approximations P. Seshadri
A. Narayan
S. Mahadevan
SIAM/ASA Journal on Uncertainty Quantification
v5, pp 1003--1023 (2017)
10.1137/16M1057668
arXiv: 1601.05470 [math.NA]
Numerical Computation of Weil--Peterson Geodesics in the Universal Teichmüller Space M. Feiszli
A. Narayan
SIAM Journal on Imaging Sciences
v10, pp 1322--1345 (2017)
10.1137/15M1043947
arXiv:1307.2358 [math.CV]
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
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]
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]
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]
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]
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]
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]
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
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]
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]
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]
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]
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
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
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
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
Sampling high dimensional optimal measures Akil Narayan
11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013
pp 902--905
AIP Publishing
10.1063/1.4825644
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
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
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
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
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)
Distributional Sensitivity for Uncertainty Quantification Akil Narayan
Dongbin Xiu
Communications in Computational Physics
v10, pp 140--160 (2011)
10.4208/cicp.160210.300710a
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