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
|