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