Edit Profile (opens in new tab) Lin, Guang Co-Author Distance Author ID: lin.guang Published as: Lin, Guang; Lin, G. Homepage: https://www.math.purdue.edu/~lin491/ External Links: MGP · ORCID Documents Indexed: 135 Publications since 2004, including 28 Additional arXiv Preprints Co-Authors: 167 Co-Authors with 134 Joint Publications 4,788 Co-Co-Authors all top 5 Co-Authors 0 single-authored 13 Zhang, Zecheng 11 Moya, Christian 8 Huang, Ziyang 8 Karniadakis, George Em 8 Zheng, Bin 7 Ardekani, Arezoo M. 7 Karagiannis, Georgios A. 7 Yang, Xiu 6 Hao, Zhaopeng 6 Konomi, Bledar A. 5 Deng, Wei 5 Hao, Wenrui 5 Li, Weixuan 5 Liang, Faming 5 Wang, Yating 5 Wang, Yuepeng 4 Leung, Wingtat 4 Mollaali, Amirhossein 4 Zeng, Lingzao 4 Zhang, Zhongqiang 3 Esquivel, Hugo 3 Jiang, Lijian 3 Li, Jinglai 3 Liu, Jiangguo 3 Ou, Na 3 Paniagua, Guillermo 3 Prakash, Arun J. 3 Su, Chau-Hsing 3 Tartakovsky, Alexandre M. 3 Wu, Laosheng 3 Xu, Zhijie 3 Xu, Zhiliang 3 Zhang, Jiahao 3 Zhang, Jiangjiang 3 Zhang, Sheng 2 Baker, Nathan A. 2 Bao, Jie 2 Bright, Ido 2 Efendiev, Yalchin R. 2 Gao, Liyao 2 Hu, Kun 2 Huang, Yao 2 Ibragimov, Ranis N. 2 Kutz, J. Nathan 2 Lei, Huan 2 Lu, Lu 2 Man, Jun 2 Navon, Ionel Michael 2 Ren, Lanlan 2 Sahin, Izzet 2 Schaeffer, Hayden 2 Shi, Xing 2 Tindel, Samy 2 Xu, Jinchao 2 Yue, Meng 2 Zhang, Shiheng 2 Zhang, Shiqi 2 Zhang, Zhidong 2 Zhang, Zongyuan 1 Bilionis, Ilias 1 Cai, Xin 1 Cai, Zhiqiang 1 Cao, Wanrong 1 Chen, Long 1 Chen, Luoping 1 Chen, Tehuan 1 Cheng, Yichen 1 Cheng, Yue 1 Choi, Minseok 1 Christlieb, Andrew J. 1 Cotilla-sanchez, Eduardo 1 Deng, Yixiang 1 Ding, Xuemei 1 Du, Huijing 1 Du, Yifan 1 Fang, Fangxin 1 Fang, Jinping 1 Fang, Zhiwei 1 Fedosov, Dmitry A. 1 Feng, Zhilan 1 Ginting, Victor 1 Grinberg, Leopold 1 Guo, Wei 1 Halappanavar, Mahantesh 1 Henager, Charles H. 1 Hesthaven, Jan S. 1 Hou, Thomas Yizhao 1 Hu, Xin 1 Huang, Zhenyu 1 Kong, Zhihao 1 LeVeque, Randall J. 1 Li, Bing 1 Li, Guanxun 1 Li, Hongshan 1 Li, Jichun 1 Li, Yuqing 1 Liao, Qifeng 1 Liu, Bangde 1 Liu, Chun 1 Liu, Jingchen ...and 67 more Co-Authors all top 5 Serials 42 Journal of Computational Physics 9 Journal of Computational and Applied Mathematics 6 Communications in Computational Physics 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Scientific Computing 4 Multiscale Modeling & Simulation 3 International Journal for Uncertainty Quantification 2 Computers and Fluids 2 Mathematical Modelling of Natural Phenomena 2 Statistics and Computing 2 Mathematics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Computers & Mathematics with Applications 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Journal of the Franklin Institute 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Journal of Statistical Planning and Inference 1 Applied Mathematics and Mechanics. (English Edition) 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Journal of Statistical Computation and Simulation 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Scientific Computing 1 Physics of Fluids 1 Optimization Methods & Software 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Statistical Analysis and Data Mining 1 Discrete and Continuous Dynamical Systems. Series S 1 Numerical Mathematics: Theory, Methods and Applications 1 Journal of Theoretical Biology 1 Journal of Applied Nonlinear Dynamics 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Fields 74 Numerical analysis (65-XX) 36 Fluid mechanics (76-XX) 28 Partial differential equations (35-XX) 23 Probability theory and stochastic processes (60-XX) 22 Statistics (62-XX) 14 Computer science (68-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Geophysics (86-XX) 6 Biology and other natural sciences (92-XX) 4 Operations research, mathematical programming (90-XX) 3 Real functions (26-XX) 3 Information and communication theory, circuits (94-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 84 Publications have been cited 746 times in 606 Documents Cited by ▼ Year ▼ Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification. Zbl 1349.76760 Bilionis, Ilias; Zabaras, Nicholas; Konomi, Bledar A.; Lin, Guang 54 2013 Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. Zbl 1408.76428 Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em 51 2012 Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity. Zbl 1349.76234 Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu 47 2014 Robust data-driven discovery of governing physical laws with error bars. Zbl 1407.62267 Zhang, Sheng; Lin, Guang 35 2018 A comparative study on the weak Galerkin, discontinuous Galerkin, and mixed finite element methods. Zbl 1295.65114 Lin, Guang; Liu, Jiangguo; Sadre-Marandi, Farrah 33 2015 Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Zbl 1320.76003 Bright, Ido; Lin, Guang; Kutz, J. Nathan 29 2013 Error analysis of finite element method for Poisson-Nernst-Planck equations. Zbl 1382.65326 Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang 26 2016 Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws. Zbl 1408.65065 Xu, Zhiliang; Liu, Yingjie; Du, Huijing; Lin, Guang; Shu, Chi-Wang 24 2011 Enhancing sparsity of Hermite polynomial expansions by iterative rotations. Zbl 1351.60041 Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang 19 2016 The stochastic piston problem. Zbl 1135.76334 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 18 2004 Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids. Zbl 1263.65006 Lin, G.; Tartakovsky, A. M.; Tartakovsky, D. M. 18 2010 ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains. Zbl 1457.65245 Winovich, Nick; Ramani, Karthik; Lin, Guang 17 2019 Predicting shock dynamics in the presence of uncertainties. Zbl 1146.76613 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 16 2006 On application of the weak Galerkin finite element method to a two-phase model for subsurface flow. Zbl 1381.76168 Ginting, Victor; Lin, Guang; Liu, Jiangguo 16 2016 Consistent, essentially conservative and balanced-force phase-field method to model incompressible two-phase flows. Zbl 1453.76131 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 16 2020 Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model. Zbl 07506632 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 16 2020 Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations. Zbl 1433.65211 Hao, Zhaopeng; Lin, Guang; Zhang, Zhongqiang 16 2020 Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach. Zbl 1416.65268 Hao, Zhaopeng; Park, Moongyu; Lin, Guang; Cai, Zhiqiang 15 2019 Numerical studies of the stochastic Korteweg-de Vries equation. Zbl 1089.65010 Lin, Guang; Grinberg, Leopold; Karniadakis, George Em 14 2006 A second-order difference scheme for the time fractional substantial diffusion equation. Zbl 1351.26014 Hao, Zhaopeng; Cao, Wanrong; Lin, Guang 12 2017 Inverse regression-based uncertainty quantification algorithms for high-dimensional models: theory and practice. Zbl 1349.62133 Li, Weixuan; Lin, Guang; Li, Bing 12 2016 Numerical solution of 3D Poisson-Nernst-Planck equations coupled with classical density functional theory for modeling ion and electron transport in a confined environment. Zbl 1388.65134 Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L. 12 2014 Constructing surrogate models of complex systems with enhanced sparsity: quantifying the influence of conformational uncertainty in biomolecular solvation. Zbl 1339.92024 Lei, H.; Yang, X.; Zheng, B.; Lin, G.; Baker, N. A. 12 2015 Stochastic modeling of random roughness in shock scattering problems: theory and simulations. Zbl 1194.76099 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 12 2008 Regularity analysis of metamaterial Maxwell’s equations with random coefficients and initial conditions. Zbl 1440.78007 Li, Jichun; Fang, Zhiwei; Lin, Guang 12 2018 Numerical studies of three-dimensional stochastic Darcy’s equation and stochastic advection-diffusion-dispersion equation. Zbl 1203.65019 Lin, Guang; Tartakovsky, A. M. 11 2010 An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling. Zbl 1349.65025 Li, Weixuan; Lin, Guang; Zhang, Dongxiao 10 2014 A Bayesian mixed shrinkage prior procedure for spatial-stochastic basis selection and evaluation of gPC expansions: applications to elliptic SPDEs. Zbl 1352.65634 Karagiannis, Georgios; Konomi, Bledar A.; Lin, Guang 10 2015 Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs. Zbl 1349.62080 Karagiannis, Georgios; Lin, Guang 9 2014 Two-level spectral methods for nonlinear elliptic equations with multiple solutions. Zbl 1398.65107 Wang, Yingwei; Hao, Wenrui; Lin, Guang 9 2018 An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. Zbl 1349.62025 Li, Weixuan; Lin, Guang 7 2015 A mixed upwind/central WENO scheme for incompressible two-phase flows. Zbl 1452.76154 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 6 2019 A consistent and conservative model and its scheme for \(N\)-phase-\(M\)-component incompressible flows. Zbl 07508530 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 6 2021 Gaussian process surrogates for failure detection: a Bayesian experimental design approach. Zbl 1349.62360 Wang, Hongqiao; Lin, Guang; Li, Jinglai 5 2016 Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs. Zbl 1349.65684 Liao, Qifeng; Lin, Guang 5 2016 An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178 Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike 5 2014 Simulated stochastic approximation annealing for global optimization with a square-root cooling schedule. Zbl 1367.62244 Liang, Faming; Cheng, Yichen; Lin, Guang 5 2014 A consistent and conservative phase-field model for thermo-gas-liquid-solid flows including liquid-solid phase change. Zbl 07524791 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 5 2022 A discontinuous Galerkin method for two-temperature plasmas. Zbl 1175.76102 Lin, Guang; Karniadakis, George Em 4 2006 A two-level stochastic collocation method for semilinear elliptic equations with random coefficients. Zbl 1404.65290 Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos 4 2017 SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations. Zbl 07511413 Zhang, Sheng; Lin, Guang 4 2021 Efficient hybrid explicit-implicit learning for multiscale problems. Zbl 07568530 Efendiev, Yalchin; Leung, Wing Tat; Lin, Guang; Zhang, Zecheng 4 2022 Real-time computational optimal control of an MHD flow system with parameter uncertainty quantification. Zbl 1451.93166 Chen, Tehuan; Ren, Zhigang; Lin, Guang; Wu, Zongze; Ye, Bao-Lin 4 2020 A consistent and conservative phase-field method for multiphase incompressible flows. Zbl 1491.76048 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 4 2022 Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Zbl 1465.65003 Xu, Zhijie; Tipireddy, Ramakrishna; Lin, Guang 4 2016 A homotopy method with adaptive basis selection for computing multiple solutions of differential equations. Zbl 07161476 Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin 4 2020 A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion. Zbl 1352.86013 Li, Jinglai; Lin, Guang; Yang, Xu 3 2015 Rare-event simulation for the stochastic Korteweg-de Vries equation. Zbl 1337.60140 Xu, Gongjun; Lin, Guang; Liu, Jingchen 3 2014 A high-order difference scheme for the fractional sub-diffusion equation. Zbl 1364.65164 Hao, Zhao-Peng; Lin, Guang; Sun, Zhi-Zhong 3 2017 Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications. Zbl 07511680 Wang, Yating; Deng, Wei; Lin, Guang 3 2021 NH-PINN: neural homogenization-based physics-informed neural network for multiscale problems. Zbl 07599595 Leung, Wing Tat; Lin, Guang; Zhang, Zecheng 3 2022 Analysis of variance-based mixed multiscale finite element method and applications in stochastic two-phase flows. Zbl 1524.76251 Wei, Jia; Lin, Guang; Jiang, Lijian; Efendiev, Yalchin 3 2014 An \(hp\)-adaptive minimum action method based on a posteriori error estimate. Zbl 1499.65025 Wan, Xiaoliang; Zheng, Bin; Lin, Guang 3 2018 Numerical solution of the Stratonovich- and Ito-Euler equations: application to the stochastic piston problem. Zbl 1286.35282 Zhang, Zhongqiang; Yang, Xiu; Lin, Guang; Karniadakis, George Em 3 2013 A low-rank approximated multiscale method for PDEs with random coefficients. Zbl 1453.65435 Ou, Na; Lin, Guang; Jiang, Lijian 3 2020 Sensitivity analysis and stochastic simulations of non-equilibrium plasma flow. Zbl 1176.76109 Lin, Guang; Karniadakis, G. E. 2 2009 Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions. Zbl 1349.60059 Zhang, Bohai; Konomi, Bledar A.; Sang, Huiyan; Karagiannis, Georgios; Lin, Guang 2 2015 A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. Zbl 1349.76472 Hao, Wenrui; Xu, Zhiliang; Liu, Chun; Lin, Guang 2 2015 Classification of spatiotemporal data via asynchronous sparse sampling: application to flow around a cylinder. Zbl 1381.37101 Bright, Ido; Lin, Guang; Kutz, J. Nathan 2 2016 Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF. Zbl 1451.62165 Wang, Yuepeng; Hu, Kun; Ren, Lanlan; Lin, Guang 2 2019 Uncertainty quantification of the gem challenge magnetic reconnection problem using the multilevel Monte Carlo method. Zbl 1498.82032 Sousa, Éder M.; Lin, Guang; Shumlak, Uri 2 2015 B-DeepONet: an enhanced Bayesian deeponet for solving noisy parametric PDEs using accelerated replica exchange SGLD. Zbl 07625386 Lin, Guang; Moya, Christian; Zhang, Zecheng 2 2023 HomPINNs: homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. Zbl 1524.65937 Huang, Yao; Hao, Wenrui; Lin, Guang 2 2022 Implementing contact angle boundary conditions for second-order phase-field models of wall-bounded multiphase flows. Zbl 07605590 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 2 2022 Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem. Zbl 1440.65065 Wang, Yuepeng; Ren, Lanlan; Zhang, Zongyuan; Lin, Guang; Xu, Chao 2 2019 Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems. Zbl 07506521 Esquivel, Hugo; Prakash, Arun; Lin, Guang 2 2021 A three-dimensional phase field model coupled with a lattice kinetics solver for modeling crystal growth in furnaces with accelerated crucible rotation and traveling magnetic field. Zbl 1390.82065 Lin, Guang; Bao, Jie; Xu, Zhijie 2 2014 Analysis of a stage-structured dengue model. Zbl 1404.92180 Fang, Jinping; Lin, Guang; Wan, Hui 2 2018 Parallel and interacting stochastic approximation annealing algorithms for global optimisation. Zbl 1384.65002 Karagiannis, Georgios; Konomi, Bledar A.; Lin, Guang; Liang, Faming 1 2017 Nonlinear analysis of perturbed rotating whirlpools in the Ocean and atmosphere. Zbl 1445.76033 Ibragimov, R. N.; Lin, G. 1 2017 A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces. Zbl 1373.82095 Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H. 1 2014 On the Bayesian calibration of computer model mixtures through experimental data, and the design of predictive models. Zbl 1376.86005 Karagiannis, Georgios; Lin, Guang 1 2017 POD-based constrained sensor placement and field reconstruction from noisy wind measurements: a perturbation study. Zbl 1397.86018 Zhang, Zhongqiang; Yang, Xiu; Lin, Guang 1 2016 Multifidelity data fusion via gradient-enhanced Gaussian process regression. Zbl 1477.62238 Deng, Yixiang; Lin, Guang; Yang, Xiu 1 2020 Assessing the effects of modeling the spectrum of clinical symptoms on the dynamics and control of Ebola. Zbl 1409.92251 Ponce, Joan; Zheng, Yiqiang; Lin, Guang; Feng, Zhilan 1 2019 An adaptive Hessian approximated stochastic gradient MCMC method. Zbl 07511683 Wang, Yating; Deng, Wei; Lin, Guang 1 2021 Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN. Zbl 07525156 Lin, Guang; Wang, Yating; Zhang, Zecheng 1 2022 RotEqNet: rotation-equivariant network for fluid systems with symmetric high-order tensors. Zbl 07525180 Gao, Liyao; Du, Yifan; Li, Hongshan; Lin, Guang 1 2022 Spectral/hp element method with hierarchical reconstruction for solving nonlinear hyperbolic conservation laws. Zbl 1212.65388 Xu, Zhiliang; Lin, Guang 1 2009 A generalized multi-fidelity simulation method using sparse polynomial chaos expansion. Zbl 1469.65023 Man, Jun; Lin, Guang; Yao, Yijun; Zeng, Lingzao 1 2021 Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements. Zbl 1503.35287 Lin, Guang; Zhang, Zecheng; Zhang, Zhidong 1 2022 Feasibility of DEIM for retrieving the initial field via dimensionality reduction. Zbl 07500740 Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang 1 2021 Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems. Zbl 1472.65012 Esquivel, Hugo; Prakash, Arun; Lin, Guang 1 2021 Calibration of reduced-order model for a coupled Burgers equations based on PC-EnKF. Zbl 1405.65130 Wang, Yuepeng; Cheng, Yue; Zhang, Zongyuan; Lin, Guang 1 2018 B-DeepONet: an enhanced Bayesian deeponet for solving noisy parametric PDEs using accelerated replica exchange SGLD. Zbl 07625386 Lin, Guang; Moya, Christian; Zhang, Zecheng 2 2023 A consistent and conservative phase-field model for thermo-gas-liquid-solid flows including liquid-solid phase change. Zbl 07524791 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 5 2022 Efficient hybrid explicit-implicit learning for multiscale problems. Zbl 07568530 Efendiev, Yalchin; Leung, Wing Tat; Lin, Guang; Zhang, Zecheng 4 2022 A consistent and conservative phase-field method for multiphase incompressible flows. Zbl 1491.76048 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 4 2022 NH-PINN: neural homogenization-based physics-informed neural network for multiscale problems. Zbl 07599595 Leung, Wing Tat; Lin, Guang; Zhang, Zecheng 3 2022 HomPINNs: homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. Zbl 1524.65937 Huang, Yao; Hao, Wenrui; Lin, Guang 2 2022 Implementing contact angle boundary conditions for second-order phase-field models of wall-bounded multiphase flows. Zbl 07605590 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 2 2022 Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN. Zbl 07525156 Lin, Guang; Wang, Yating; Zhang, Zecheng 1 2022 RotEqNet: rotation-equivariant network for fluid systems with symmetric high-order tensors. Zbl 07525180 Gao, Liyao; Du, Yifan; Li, Hongshan; Lin, Guang 1 2022 Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements. Zbl 1503.35287 Lin, Guang; Zhang, Zecheng; Zhang, Zhidong 1 2022 A consistent and conservative model and its scheme for \(N\)-phase-\(M\)-component incompressible flows. Zbl 07508530 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 6 2021 SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations. Zbl 07511413 Zhang, Sheng; Lin, Guang 4 2021 Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications. Zbl 07511680 Wang, Yating; Deng, Wei; Lin, Guang 3 2021 Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems. Zbl 07506521 Esquivel, Hugo; Prakash, Arun; Lin, Guang 2 2021 An adaptive Hessian approximated stochastic gradient MCMC method. Zbl 07511683 Wang, Yating; Deng, Wei; Lin, Guang 1 2021 A generalized multi-fidelity simulation method using sparse polynomial chaos expansion. Zbl 1469.65023 Man, Jun; Lin, Guang; Yao, Yijun; Zeng, Lingzao 1 2021 Feasibility of DEIM for retrieving the initial field via dimensionality reduction. Zbl 07500740 Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang 1 2021 Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems. Zbl 1472.65012 Esquivel, Hugo; Prakash, Arun; Lin, Guang 1 2021 Consistent, essentially conservative and balanced-force phase-field method to model incompressible two-phase flows. Zbl 1453.76131 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 16 2020 Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model. Zbl 07506632 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 16 2020 Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations. Zbl 1433.65211 Hao, Zhaopeng; Lin, Guang; Zhang, Zhongqiang 16 2020 Real-time computational optimal control of an MHD flow system with parameter uncertainty quantification. Zbl 1451.93166 Chen, Tehuan; Ren, Zhigang; Lin, Guang; Wu, Zongze; Ye, Bao-Lin 4 2020 A homotopy method with adaptive basis selection for computing multiple solutions of differential equations. Zbl 07161476 Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin 4 2020 A low-rank approximated multiscale method for PDEs with random coefficients. Zbl 1453.65435 Ou, Na; Lin, Guang; Jiang, Lijian 3 2020 Multifidelity data fusion via gradient-enhanced Gaussian process regression. Zbl 1477.62238 Deng, Yixiang; Lin, Guang; Yang, Xiu 1 2020 ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains. Zbl 1457.65245 Winovich, Nick; Ramani, Karthik; Lin, Guang 17 2019 Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach. Zbl 1416.65268 Hao, Zhaopeng; Park, Moongyu; Lin, Guang; Cai, Zhiqiang 15 2019 A mixed upwind/central WENO scheme for incompressible two-phase flows. Zbl 1452.76154 Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. 6 2019 Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF. Zbl 1451.62165 Wang, Yuepeng; Hu, Kun; Ren, Lanlan; Lin, Guang 2 2019 Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem. Zbl 1440.65065 Wang, Yuepeng; Ren, Lanlan; Zhang, Zongyuan; Lin, Guang; Xu, Chao 2 2019 Assessing the effects of modeling the spectrum of clinical symptoms on the dynamics and control of Ebola. Zbl 1409.92251 Ponce, Joan; Zheng, Yiqiang; Lin, Guang; Feng, Zhilan 1 2019 Robust data-driven discovery of governing physical laws with error bars. Zbl 1407.62267 Zhang, Sheng; Lin, Guang 35 2018 Regularity analysis of metamaterial Maxwell’s equations with random coefficients and initial conditions. Zbl 1440.78007 Li, Jichun; Fang, Zhiwei; Lin, Guang 12 2018 Two-level spectral methods for nonlinear elliptic equations with multiple solutions. Zbl 1398.65107 Wang, Yingwei; Hao, Wenrui; Lin, Guang 9 2018 An \(hp\)-adaptive minimum action method based on a posteriori error estimate. Zbl 1499.65025 Wan, Xiaoliang; Zheng, Bin; Lin, Guang 3 2018 Analysis of a stage-structured dengue model. Zbl 1404.92180 Fang, Jinping; Lin, Guang; Wan, Hui 2 2018 Calibration of reduced-order model for a coupled Burgers equations based on PC-EnKF. Zbl 1405.65130 Wang, Yuepeng; Cheng, Yue; Zhang, Zongyuan; Lin, Guang 1 2018 A second-order difference scheme for the time fractional substantial diffusion equation. Zbl 1351.26014 Hao, Zhaopeng; Cao, Wanrong; Lin, Guang 12 2017 A two-level stochastic collocation method for semilinear elliptic equations with random coefficients. Zbl 1404.65290 Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos 4 2017 A high-order difference scheme for the fractional sub-diffusion equation. Zbl 1364.65164 Hao, Zhao-Peng; Lin, Guang; Sun, Zhi-Zhong 3 2017 Parallel and interacting stochastic approximation annealing algorithms for global optimisation. Zbl 1384.65002 Karagiannis, Georgios; Konomi, Bledar A.; Lin, Guang; Liang, Faming 1 2017 Nonlinear analysis of perturbed rotating whirlpools in the Ocean and atmosphere. Zbl 1445.76033 Ibragimov, R. N.; Lin, G. 1 2017 On the Bayesian calibration of computer model mixtures through experimental data, and the design of predictive models. Zbl 1376.86005 Karagiannis, Georgios; Lin, Guang 1 2017 Error analysis of finite element method for Poisson-Nernst-Planck equations. Zbl 1382.65326 Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang 26 2016 Enhancing sparsity of Hermite polynomial expansions by iterative rotations. Zbl 1351.60041 Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang 19 2016 On application of the weak Galerkin finite element method to a two-phase model for subsurface flow. Zbl 1381.76168 Ginting, Victor; Lin, Guang; Liu, Jiangguo 16 2016 Inverse regression-based uncertainty quantification algorithms for high-dimensional models: theory and practice. Zbl 1349.62133 Li, Weixuan; Lin, Guang; Li, Bing 12 2016 Gaussian process surrogates for failure detection: a Bayesian experimental design approach. Zbl 1349.62360 Wang, Hongqiao; Lin, Guang; Li, Jinglai 5 2016 Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs. Zbl 1349.65684 Liao, Qifeng; Lin, Guang 5 2016 Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Zbl 1465.65003 Xu, Zhijie; Tipireddy, Ramakrishna; Lin, Guang 4 2016 Classification of spatiotemporal data via asynchronous sparse sampling: application to flow around a cylinder. Zbl 1381.37101 Bright, Ido; Lin, Guang; Kutz, J. Nathan 2 2016 POD-based constrained sensor placement and field reconstruction from noisy wind measurements: a perturbation study. Zbl 1397.86018 Zhang, Zhongqiang; Yang, Xiu; Lin, Guang 1 2016 A comparative study on the weak Galerkin, discontinuous Galerkin, and mixed finite element methods. Zbl 1295.65114 Lin, Guang; Liu, Jiangguo; Sadre-Marandi, Farrah 33 2015 Constructing surrogate models of complex systems with enhanced sparsity: quantifying the influence of conformational uncertainty in biomolecular solvation. Zbl 1339.92024 Lei, H.; Yang, X.; Zheng, B.; Lin, G.; Baker, N. A. 12 2015 A Bayesian mixed shrinkage prior procedure for spatial-stochastic basis selection and evaluation of gPC expansions: applications to elliptic SPDEs. Zbl 1352.65634 Karagiannis, Georgios; Konomi, Bledar A.; Lin, Guang 10 2015 An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. Zbl 1349.62025 Li, Weixuan; Lin, Guang 7 2015 A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion. Zbl 1352.86013 Li, Jinglai; Lin, Guang; Yang, Xu 3 2015 Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions. Zbl 1349.60059 Zhang, Bohai; Konomi, Bledar A.; Sang, Huiyan; Karagiannis, Georgios; Lin, Guang 2 2015 A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. Zbl 1349.76472 Hao, Wenrui; Xu, Zhiliang; Liu, Chun; Lin, Guang 2 2015 Uncertainty quantification of the gem challenge magnetic reconnection problem using the multilevel Monte Carlo method. Zbl 1498.82032 Sousa, Éder M.; Lin, Guang; Shumlak, Uri 2 2015 Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity. Zbl 1349.76234 Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu 47 2014 Numerical solution of 3D Poisson-Nernst-Planck equations coupled with classical density functional theory for modeling ion and electron transport in a confined environment. Zbl 1388.65134 Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L. 12 2014 An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling. Zbl 1349.65025 Li, Weixuan; Lin, Guang; Zhang, Dongxiao 10 2014 Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs. Zbl 1349.62080 Karagiannis, Georgios; Lin, Guang 9 2014 An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178 Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike 5 2014 Simulated stochastic approximation annealing for global optimization with a square-root cooling schedule. Zbl 1367.62244 Liang, Faming; Cheng, Yichen; Lin, Guang 5 2014 Rare-event simulation for the stochastic Korteweg-de Vries equation. Zbl 1337.60140 Xu, Gongjun; Lin, Guang; Liu, Jingchen 3 2014 Analysis of variance-based mixed multiscale finite element method and applications in stochastic two-phase flows. Zbl 1524.76251 Wei, Jia; Lin, Guang; Jiang, Lijian; Efendiev, Yalchin 3 2014 A three-dimensional phase field model coupled with a lattice kinetics solver for modeling crystal growth in furnaces with accelerated crucible rotation and traveling magnetic field. Zbl 1390.82065 Lin, Guang; Bao, Jie; Xu, Zhijie 2 2014 A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces. Zbl 1373.82095 Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H. 1 2014 Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification. Zbl 1349.76760 Bilionis, Ilias; Zabaras, Nicholas; Konomi, Bledar A.; Lin, Guang 54 2013 Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Zbl 1320.76003 Bright, Ido; Lin, Guang; Kutz, J. Nathan 29 2013 Numerical solution of the Stratonovich- and Ito-Euler equations: application to the stochastic piston problem. Zbl 1286.35282 Zhang, Zhongqiang; Yang, Xiu; Lin, Guang; Karniadakis, George Em 3 2013 Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. Zbl 1408.76428 Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em 51 2012 Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws. Zbl 1408.65065 Xu, Zhiliang; Liu, Yingjie; Du, Huijing; Lin, Guang; Shu, Chi-Wang 24 2011 Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids. Zbl 1263.65006 Lin, G.; Tartakovsky, A. M.; Tartakovsky, D. M. 18 2010 Numerical studies of three-dimensional stochastic Darcy’s equation and stochastic advection-diffusion-dispersion equation. Zbl 1203.65019 Lin, Guang; Tartakovsky, A. M. 11 2010 Sensitivity analysis and stochastic simulations of non-equilibrium plasma flow. Zbl 1176.76109 Lin, Guang; Karniadakis, G. E. 2 2009 Spectral/hp element method with hierarchical reconstruction for solving nonlinear hyperbolic conservation laws. Zbl 1212.65388 Xu, Zhiliang; Lin, Guang 1 2009 Stochastic modeling of random roughness in shock scattering problems: theory and simulations. Zbl 1194.76099 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 12 2008 Predicting shock dynamics in the presence of uncertainties. Zbl 1146.76613 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 16 2006 Numerical studies of the stochastic Korteweg-de Vries equation. Zbl 1089.65010 Lin, Guang; Grinberg, Leopold; Karniadakis, George Em 14 2006 A discontinuous Galerkin method for two-temperature plasmas. Zbl 1175.76102 Lin, Guang; Karniadakis, George Em 4 2006 The stochastic piston problem. Zbl 1135.76334 Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. 18 2004 all cited Publications top 5 cited Publications all top 5 Cited by 1,154 Authors 47 Lin, Guang 17 Karniadakis, George Em 13 Zhang, Shangyou 12 Kutz, J. Nathan 12 Yang, Xiu 12 Zabaras, Nicholas J. 11 Ye, Xiu 10 Tartakovsky, Alexandre M. 9 Brunton, Steven L. 9 Liu, Jiangguo 8 Bilionis, Ilias 8 Liao, Qifeng 8 Wang, Hong 8 Zheng, Xiangcheng 7 Ervin, Vincent J. 7 Gao, Fuzheng 7 Hao, Wenrui 7 Huang, Ziyang 7 Zhang, Tie 6 Ardekani, Arezoo M. 6 Doostan, Alireza 6 Kim, Junseok 6 Koutsourelakis, Phaedon-Stelios 6 Tavener, Simon J. 6 Yang, Junxiang 6 Yang, Ying 6 Zhang, Dongxiao 6 Zhang, Zhongqiang 6 Zhou, Shenggao 5 Chakraborty, Souvik 5 Dong, Suchuan 5 Hao, Zhaopeng 5 Jiang, Lijian 5 Kumar, Naresh 5 Li, Jichun 5 Li, Jinglai 5 Mishra, Siddhartha 5 Schwab, Christoph 5 Tartakovsky, Daniel M. 5 Wang, Yuepeng 4 Abgrall, Rémi 4 Babaee, Hessam 4 Baker, Nathan A. 4 Cao, Wanrong 4 Chen, Zhangxin 4 Chung, Tsz Shun Eric 4 Congedo, Pietro Marco 4 Deka, Bhupen 4 Karagiannis, Georgios A. 4 Konomi, Bledar A. 4 Lei, Huan 4 Leung, Wingtat 4 Li, Shengyue 4 Li, Weixuan 4 Liu, Chun 4 Liu, Yingjie 4 Lu, Benzhuo 4 Lucor, Didier 4 Luo, Hong 4 Mani, Ali 4 Mu, Lin 4 Rui, Hongxing 4 Schaeffer, Hayden 4 Šukys, Jonas 4 Tang, Kunkun 4 Tipireddy, Ramakrishna 4 Wang, Junping 4 Wang, Xiaoshen 4 Wang, Yating 4 Wang, Zhongming 4 Wang, Zhuoran 4 Xu, Hao 4 Xu, Zhiliang 4 Zhai, Qilong 4 Zhong, Liuqiang 3 Barajas-Solano, David A. 3 Chen, Minghua 3 Chen, Yanping 3 Cheung, Siu Wun 3 Cho, Heyrim 3 Constantine, Paul G. 3 Cortés López, Juan Carlos 3 Després, Bruno 3 Du, Ning 3 Duan, Jinqiao 3 Fang, Zhiwei 3 Girolami, Mark A. 3 Glaws, Andrew 3 Gu, Yiqi 3 Hampton, Jerrad 3 He, Yinnian 3 Huang, Yunqing 3 Kaiser, Eurika 3 Kim, Chongam 3 Li, Jian 3 Lin, Tao 3 Lu, Linzhang 3 Lü, Zhenzhou 3 Ma, Jie 3 Nair, Prasanth B. ...and 1,054 more Authors all top 5 Cited in 128 Serials 163 Journal of Computational Physics 41 Computer Methods in Applied Mechanics and Engineering 39 Journal of Computational and Applied Mathematics 39 Journal of Scientific Computing 20 Computers & Mathematics with Applications 20 SIAM Journal on Scientific Computing 16 SIAM/ASA Journal on Uncertainty Quantification 14 Applied Numerical Mathematics 11 Computers and Fluids 11 Applied Mathematics and Computation 11 Multiscale Modeling & Simulation 9 Communications in Computational Physics 8 Numerical Methods for Partial Differential Equations 8 Computational Geosciences 7 Numerical Algorithms 6 Journal of Fluid Mechanics 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Mathematics of Computation 4 International Journal for Numerical Methods in Engineering 4 Computational Mechanics 4 SIAM Journal on Applied Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Advances in Applied Mathematics and Mechanics 3 Physica D 3 Applied Mathematics Letters 3 Applied Mathematical Modelling 3 Advances in Computational Mathematics 3 Mathematical Problems in Engineering 3 Chaos 3 Communications in Nonlinear Science and Numerical Simulation 3 Discrete and Continuous Dynamical Systems. Series B 3 SIAM Journal on Applied Dynamical Systems 3 Statistics and Computing 3 Communications on Applied Mathematics and Computation 2 Computer Physics Communications 2 Journal of the Franklin Institute 2 Journal of Mathematical Analysis and Applications 2 Physica A 2 Bulletin of Mathematical Biology 2 Chaos, Solitons and Fractals 2 Journal of Differential Equations 2 Mathematics and Computers in Simulation 2 Optimal Control Applications & Methods 2 Computational Statistics 2 Nonlinear Dynamics 2 Archives of Computational Methods in Engineering 2 Acta Mathematica Scientia. Series B. (English Edition) 2 International Journal of Computational Methods 2 International Journal of Numerical Analysis and Modeling 2 Engineering Optimization 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Agricultural, Biological, and Environmental Statistics 2 Journal of Theoretical Biology 2 Mathematical Sciences 2 Sampling Theory, Signal Processing, and Data Analysis 1 Acta Mechanica 1 Inverse Problems 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Mathematical Methods in the Applied Sciences 1 Wave Motion 1 BIT 1 Calcolo 1 Journal of Multivariate Analysis 1 Journal of Optimization Theory and Applications 1 Journal of Statistical Planning and Inference 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Mathematica Numerica Sinica 1 Revista Colombiana de Estadística 1 Journal of Computational Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Integral Equations and Applications 1 Neural Networks 1 Machine Learning 1 The Annals of Applied Probability 1 Communications in Statistics. Simulation and Computation 1 SIAM Review 1 Computational Statistics and Data Analysis 1 International Journal of Robust and Nonlinear Control 1 Journal of Mathematical Imaging and Vision 1 International Journal of Computer Vision 1 Computational and Applied Mathematics 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Turkish Journal of Mathematics 1 Engineering Analysis with Boundary Elements 1 Bernoulli 1 Journal of Mathematical Chemistry 1 Differential Equations and Dynamical Systems 1 Abstract and Applied Analysis 1 Optimization Methods & Software 1 Fractional Calculus & Applied Analysis 1 Journal of Applied Statistics 1 Journal of Biological Systems 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Nonlinear Analysis. Real World Applications 1 Quantitative Finance ...and 28 more Serials all top 5 Cited in 36 Fields 425 Numerical analysis (65-XX) 235 Partial differential equations (35-XX) 170 Fluid mechanics (76-XX) 107 Statistics (62-XX) 92 Probability theory and stochastic processes (60-XX) 83 Computer science (68-XX) 29 Mechanics of deformable solids (74-XX) 28 Biology and other natural sciences (92-XX) 24 Optics, electromagnetic theory (78-XX) 22 Real functions (26-XX) 22 Dynamical systems and ergodic theory (37-XX) 17 Ordinary differential equations (34-XX) 17 Statistical mechanics, structure of matter (82-XX) 17 Geophysics (86-XX) 15 Systems theory; control (93-XX) 14 Approximations and expansions (41-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 10 Special functions (33-XX) 10 Operations research, mathematical programming (90-XX) 10 Information and communication theory, circuits (94-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Mechanics of particles and systems (70-XX) 5 Classical thermodynamics, heat transfer (80-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year