M. Yang, P. Wang, M. Fan, D. Lu, Y. Cao, G. Zhang, Conditional pseudo-reversible normalizing flow for surrogate modeling in quantifying uncertainty propagation, Journal of Machine Learning for Modeling and Computing, 6(4), pp. 1-28, 2025 (DOI: 10.1615/JMachLearnModelComput.2025060260)

M. Fan, Z. Zhang, D. Lu, G. Zhang, GenAI4UQ: A software for inverse uncertainty quantification using conditional generative AI models, SoftwareX, 31, 102232, 2025 (DOI: 10.1016/j.softx.2025.102232).

S. Liang, R. Hu, F. Bao, R. Archibald, G. Zhang, Assimilating Partial Observation to Enhance Feedback Control of Stochastic Dynamical Systems, Foundations of Data Science, 2025 (DOI: 10.3934/fods.2025010).

F. Bao, H. Chipilski, S. Liang, G. Zhang, J. Whitaker, Nonlinear ensemble filtering with diffusion models: application to the surface quasi-geostrophic dynamics, Monthly Weather Review, 153(7), pp. 1155–1169, 2025. (DOI: 10.1175/MWR-D-24-0069.1)

T. Huynh, T. Hoang, G. Zhang, F. Bao, Joint State-Parameter Estimation for the Reduced Fracture Model via the United Filter, Journal of Computational Physics, 538, 114159, 2025. (DOI: 10.1016/j.jcp.2025.114159)

Y. Geng, O. Burkovska, L. Ju, G. Zhang, M. Gunzburger, An End-to-End Deep Learning Method for Solving Nonlocal Allen-Cahn and Cahn-Hilliard Phase-Field Models, Computer Methods in Applied Mechanics and Engineering, 436, 117721, 2025. (DOI: 10.1016/j.cma.2024.117721)

H. Tran, Q. Du, G. Zhang, Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing, Computational Optimization and Applications, 2025. (DOI: 10.1007/s10589-024-00641-0)

J. Yin, V. Reshniak, S. Liu, G. Zhang,  X. Wang, Z. Xiao, Z. Morgan, S. Pawledzio, T. Proffen, C. Hoffmann, H. Cao, B. Chakoumakos, Y. Liu, Integrated edge-to-exascale workflow for real-time steering in neutron scattering experiments, Structural Dynamics, 11(6), 2024. (DOI: 10.1063/4.0000279)

Z. Shi, H. Ma, H. Tran, G. Zhang, Compressive-sensing-assisted mixed integer optimization for dynamical system discovery with highly noisy data, Numerical Methods for Partial Differential Equations, 41(1), e23164, 2025. (DOI: 10.1002/num.23164)

Y. Liu, A. Bryantseva, M. Stoyanov, F. Bao, G. Zhang, Diffusion-based sparse-grid generative models for density estimation,  Applied Mathematics for Modern Challenges, 2(4), pp. 365-381, 2024. (DOI: 10.3934/ammc.2024019)

M. Fan, Y. Liu, D. Lu, H. Wang, G. Zhang, A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage, Journal of Hydrology, 648, 132323, 2025. (DOI: 10.1016/j.jhydrol.2024.132323)

F. Bao, Z. Zhang, G. Zhang, An ensemble score filter for tracking high-dimensional nonlinear dynamical system, Computer Methods in Applied Mechanics and Engineering, 432, Part B, 117447, 2024. (DOI:10.1016/j.cma.2024.117447)

J. Smith, H. Tran, K. Roccapriore, Z. Shen, G. Zhang, M. Chi, 4D-STEM Compressive Sensing and Dynamic Sampling for Interfaces in Beam Sensitive Materials, Small Methods, 2400742, 2024. (DOI:10.1002/smtd.202400742)

D. Lu, Y. Liu, Z. Zhang, F. Bao, G. Zhang, A diffusion-based uncertainty quantification method to advance E3SM model calibration, Journal of Geophysical Research: Machine Learning and Computation, 1,  e2024JH000234, 2024. (DOI:10.1029/2024JH000234)

F. Bao, Z. Zhang, G. Zhang, A score-based filter for nonlinear data assimilation, Journal of Computational Physics, 514, 113207, 2024. (DOI:10.1016/j.jcp.2024.113207)

Z. Zhang, F. Bao, G. Zhang, Improving the expressive power of deep neural networks through integral activation transform, International Journal of Numerical Analysis and Modeling, 21(5), pp. 739-763, 2024. (DOI:10.4208/ijnam2024-1030)

M. Yang, P. Wang, D. del-Castillo-Negrete, Y. Cao, G. Zhang, A pseudo-reversible normalizing flow for stochastic dynamical systems with various initial conditions, SIAM Journal on Scientific Computing, 46(4), pp. C508-C533, 2024. (DOI:10.1137/23M1585635)

Z. Zhang, F. Bao, L. Ju, G. Zhang, Transferable neural networks for partial differential equations, Journal of Scientific Computing, 99 (2), pp. 1-25, 2024. (DOI:10.1007/s10915-024-02463-y)

Y. Liu, M. Yang, Z. Zhang, F. Bao, Y. Cao, G. Zhang, Diffusion-model-assisted supervised learning of generative models for density estimation, Journal of Machine Learning for Modeling and Computing, 5(1), pp. 25-38, 2024. (DOI:10.1615/JMachLearnModelComput.2024051346)

H. Ni, Z. Wu, X. Wu, J. Smith, M. Zachman, J. Zuo, L. Ju, G. Zhang, M. Chi, Quantifying atomically dispersed catalysts using deep learning assisted microscopy analysis, Nano Letters, 23(16), pp. 7442-7448, 2023. (DOI:10.1021/acs.nanolett.3c01892)

M. Yang, D. del-Castillo-Negrete, Y. Cao, G. Zhang, A probabilistic scheme for semilinear nonlocal diffusion equations with volume constraints, SIAM Journal on Numerical Analysis, 61(6), pp. 2718-2743, 2023. (DOI:10.1137/22M1494877)

Q. Ma, X. Bai, E. Feng, G. Zhang, H. Cao, CrysFieldExplorer: rapid optimization of crystal field Hamiltonian, Journal of Applied Crystallography, 56 (4), pp. 1229-1241, 2023. (DOI:10.1107/S1600576723005897)

J. Smith, Z. Huang, W. Gao, G. Zhang, M. Chi, Atomic resolution cryogenic 4D-STEM imaging robust distortion correction, ACS Nano, Vol 17, pp. 11327-11334, 2023. (DOI:10.1021/acsnano.2c12777)

Y. Teng, Z. Wang, L. Ju, A. Gruber, G. Zhang, Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation, SIAM Journal on Scientific Computing, Vol 45(3), pp. A1148-A1171, 2023. (DOI:10.1137/21M1459198)

J. Yin, S. Liu, V. Rashniak, X. Wang, G. Zhang, A scalable transformer model for real-time decision making in neutron scattering experiments, Journal of Machine Learning for Modeling and Computing, 4(1), pp. 95-107, 2023. (DOI:10.1615/JMachLearnModelComput.2023048607)

Y. Hao, E. Feng, D. Lu, L. Zimmer, Z. Morgan, B. Chakoumakos, G. Zhang, H. Cao, Machine-learning-assisted automation of single-crystal neutron diffraction, Journal of Applied Crystallography, 56, pp. 519-525, 2023. (DOI:10.1107/S1600576723001516)

M. Yang, D. del-Castillo-Negrete, G. Zhang, and M. T. Beidler , A divergence-free constrained magnetic field interpolation method for scattered data, Physics of Plasmas, 30, 033901, 2023. (DOI:10.1063/5.0138905)

M. Radaideh, H. Tran, L. Lin, H. Jiang, D. Winder, S. Gorti, G. Zhang, J. Mach, S. Cousineau, Model Calibration of the Liquid Mercury Spallation Target using Evolutionary Neural Networks and Sparse Polynomial Expansions, Nuclear Inst. and Methods in Physics Research B, 525(15), pp. 41-54, 2022. (DOI:10.1016/j.nimb.2022.06.001)

S. Bi, B. Stump, J. Zhang, Y. Lee, J. Coleman, M. Bement, G. Zhang, Black-box optimization for approximating high-fidelity heat transfer calculations in metal additive manufacturing, Results in Materials, 13, 100258, 2022. (DOI:10.1016/j.rinma.2022.100258)

P. Zhang, S. Liu, D. Lu, R. Sankaran, G. Zhang, An out-of-distribution-aware autoencoder model for reduced chemical kinetics, Discrete & Continuous Dynamical Systems - Series S, 15(4), pp. 913-930, 2022. (DOI:10.3934/dcdss.2021138)

G. Zhang, L. Mu, A non-intrusive domain-decomposition model reduction method for linear steady-state PDEs with random coefficients, Numerical Methods for Partial Differential Equations, 38, pp. 1993-2011, 2022. (DOI:10.1002/num.22856)

J. Zhang, H. Tran, and G. Zhang, Accelerating Reinforcement Learning with a Directional-Gaussian-Smoothing Evolution Strategy, Electronic Research Archive, 29(6), pp. 4119-4135, 2021. (DOI:10.3934/era.2021075)

M. Yang, G. Zhang, D. del-Castillo-Negrete and M. Stoyanov, A Feynman-Kac based numerical method for the exit time probability of a class of transport problems, Journal of Computational Physics, 444, 110564, 2021. (DOI:10.1016/j.jcp.2021.110564)

J. Zhang, S. Bi, and G. Zhang, A directional Gaussian smoothing optimization method for computational inverse design in nanophotonics, Materials & Design, 197 (1), 109213, 2021. (DOI:10.1016/j.matdes.2020.109213)

M. Yang, G. Zhang, D. del-Castillo-Negrete, M. Stoyanov, and M. Beidler, A sparse-grid probabilistic scheme for approximation of the runaway probability of electrons in fusion tokamak simulation, Springer Lecture Notes on CS&E, 144, pp. 245-264, 2021. (DOI:10.1007/978-3-030-81362-8_11)

J. Zhang, X. Liu, S. Bi, J. Yi, G. Zhang, M. Eisenbach, Robust data-driven approach for predicting the configurational energy of high entropy alloys, Material & Design, 185 (5), 108247, 2020. (DOI:10.1016/j.matdes.2019.108247)

L. Mu and G. Zhang, A domain-decomposition model reduction method for linear convection- diffusion equations with random coefficients, SIAM Journal on Scientific Computing, 41 (3), pp. A1984-A2011, 2019. (DOI:10.1137/18M1170601)

X. Xie, G. Zhang and C. Webster, Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network, Mathematics, 7(8), 757, 2019. (DOI:10.3390/math7080757)

M. Gunzburger, M. Schneier, C. Webster, and G. Zhang, An improved discrete least-squares/reduced-basis method for parameterized elliptic PDEs, Journal of Scientific Computing, 81 (1), pp. 76-91, 2019. (DOI:10.1007/s10915-018-0661-6)

P. Jantsch, C. Webster and G. Zhang, On the Lebesgue constants of weighted Leja points for Lagrange interpolation on unbounded domains, IMA Journal on Numerical Analysis, 39 (2), 1039-1057, 2019.  (DOI:10.1093/imanum/dry002)

E. Hirvijoki, C. Liu, G. Zhang, D. del-Castillo-Negrete, and D. Brennan, A fluid-kinetic framework for self-consistent runaway-electron simulations, Physics of Plasmas, 25, 062507, 2018. (DOI:10.1063/1.5030424) 

J. Yang, G. Zhang and W. Zhao, A first-order numerical scheme for forward-backward stochastic differential equations in bounded domains, Journal of Computational Mathematics, 36(2), pp. 237-258, 2018. (DOI:10.4208/jcm.1612-m2016-0582)

S. Mo, D. Lu, X. Shi, G. Zhang, M. Ye, J. Wu and J. Wu, A Taylor expansion-based adaptive design strategy for global surrogate modeling with applications in multiphase flow simulation, Water Resources Research, 53, pp. 10802-10823, 2017. (DOI:10.1002/2017WR021622)

H. Tran, C. Webster and G. Zhang, Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients, Numerishe Mathematik, 137, pp. 451-493, 2017. (DOI:10.1007/s00211-017-0878-6)

G. Zhang, and D. del-Castillo-Negrete, A backward Monte-Carlo method for time-dependent runaway electron simulations, Physics of Plasmas, 24, 092511, 2017. (DOI:10.1063/1.4986019)

W. Zhao, W. Zhang and G. Zhang, Second-order numerical schemes for decoupled forward-backward stochastic differential equations with jumps, Journal of Computational Mathematics, 35(4), pp. 213-244, 2017. (DOI:10.4208/jcm.1612-m2015-0245)

Q. Guan, M. Gunzburger, C. Webster and G. Zhang, Reduced basis methods for nonlocal diffusion problems with random input data, Computer Methods in Applied Mechanics and Engineering, 317(15), pp. 746-770, 2017. (DOI:10.1016/j.cma.2016.12.019)

M. Xi, D. Lu, D. Gui, Z. Qi and G. Zhang, Calibration of an agricultural-hydrological model (RZWQM2) using surrogate global optimization, Journal of Hydrology, 544, pp. 456-466, 2017. (DOI:10.1016/j.jhydrol.2016.11.051)

D. Lu, G. Zhang, C. Webster and C. Barbier, An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations, Water Resources Research, 52 (12), pp. 9642-9660, 2016. (DOI:10.1002/2016WR019475)

F. Bao, Y. Tang, M. Summers, G. Zhang, C. Webster, V. Scarola and T.A. Maier, Efficient stochastic optimization for analytic continuation, Physical Review B, 94, 125149, 2016. (DOI:10.1103/PhysRevB.94.125149)

D. Galindo, P. Jantsch, C. Webster and G. Zhang, Accelerating hierarchical stochastic collocation methods for partial differential equations with random input data, SIAM/ASA Journal on Uncertainty Quantification, 4 (1), pp. 1111-1137, 2016. (DOI:10.1137/15M1019568)

G. Zhang, C. Webster, M. Gunzburger and J. Burkardt, Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection, SIAM Review, 58 (3), pp. 517-551, 2016. (DOI:10.1137/16M1071699)

F. Bao, Y. Cao, C. Webster and G. Zhang, An efficient meshfree implicit filter for nonlinear filtering problems, International Journal for Uncertainty Quantification, 6 (1), pp. 19-33, 2016. (DOI:10.1615/Int.J.UncertaintyQuantification.2016013870) 

G. Zhang, W. Zhao, M. Gunzburger and C. Webster, Numerical methods for a class of nonlocal diffusion problems with the use of backward SDEs, Computers & Mathematics with Applications, 71 (11), pp. 2479-2496, 2016. (DOI:10.1016/j.camwa.2015.11.002)

H. Tran, C. Webster and G. Zhang, A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models, Springer Lecture Notes on CS&E, 109, pp. 291-313, 2016. (DOI:10.1007/978-3-319-28262-6_12)

N. Dexter, C. Webster and G. Zhang, Explicit cost bounds of stochastic Galerkin approximations for parametertized PDEs with random coefficients, Computers & Mathematics with Applications, 71 (11), pp. 2231-2256, 2016. (DOI:10.1016/j.camwa.2015.12.005)

G. Zhang, C. Webster, M. Gunzburger and J. Burkardt, A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection, SIAM Journal of Numerical Analysis, 53 (3), pp. 1508-1536, 2015. (DOI:10.1137/140971531)

M. Gunzburger, C. Webster and G. Zhang, Sparse collocation methods for stochastic interpolation and quadrature, Handbook of Uncertainty Quantification, pp. 717-762, Springer International Publishing, Switzerland, 2016. (DOI:10.1007/978-3-319-12385-1_29)

V. Reshniak, A. Khaliq, D. Voss and G. Zhang, Split-step Milstein methods for multi-channel stiff stochastic differential systems, Applied Numerical Mathematics, 89, pp. 1-23, 2015. (DOI:10.1016/j.apnum.2014.10.005)

F. Bao, Y. Cao, C. Webster and G. Zhang, A hybrid sparse-grid approach for nonlinear filtering problems based on adaptive domain of the Zakai equation approximations, SIAM/ASA Journal on Uncertainty Quantification, 2 (1), pp. 784-804, 2014. (DOI:10.1137/140952910) 

M. Gunzburger, C. Webster and G. Zhang, Stochastic finite element methods for partial differential equations with random input data, Acta Numerica, 23, pp. 521-650, 2014. (DOI:10.1017/S0962492914000075)

C. Webster, G. Zhang and M. Gunzburger, An adaptive sparse-grid-based iterative ensemble Kalman filter approach for parameter field estimation, International Journal of Computer Mathematics, 91 (4), pp. 798-817, 2014. (DOI:10.1080/00207160.2013.854339) 

X. Zhang, C. Liu, B. Hu and G. Zhang, Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments, Journal of Contaminant Hydrology, 156, pp. 1-15, 2014. (DOI:10.1016/j.jconhyd.2013.10.001)

M. Gunzburger, C. Webster, G. Zhang, An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data, Springer Lecture Notes on CS&E, 97, pp. 137-170, 2014. (DOI:10.1007/978-3-319-04537-5_6)

G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster, An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling, Water Resources Research, 49(10), pp. 6871-6892, 2013. (DOI:10.1002/wrcr.20467)

G. Zhang, M. Gunzburger and W. Zhao, A sparse-grid method for multi-dimensional backward stochastic differential equations, Journal of Computational Mathematics, 31 (3), pp. 221-248, 2013. (DOI:10.4208/jcm.1212-m4014) 

G. Zhang and M. Gunzburger, Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data, SIAM Journal on Numerical Analysis, 50 (4), pp. 1922-1940, 2012. (DOI:10.1137/11084306X) 

W. Zhao, Y. Li and G. Zhang, A generalized theta-scheme for solving backward stochastic differential equations, Discrete and Continuous Dynamical Systems - Series B, 17 (5), pp. 1585-1603, 2012. (DOI:10.3934/dcdsb.2012.17.1585)

W. Zhao, G. Zhang and L. Ju, A stable multi-step scheme for solving backward stochastic differential equations, SIAM Journal on Numerical Analysis, 48 (4), pp. 1369-1394, 2010. (DOI:10.1137/09076979X)

H. Rafid, J. Yin, Y. Geng, S. Liang, F. Bao, L. Ju, G. Zhang, A Scalable Training-Free Diffusion Model for Uncertainty Quantification, Proceedings of the SC '24 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis, 2024. [Download, DOI:10.1109/SCW63240.2024.00057]

J. Yin, S. Liang, S. Liu, F. Bao, H. Chipilski, D. Lu, G. Zhang, A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics, Proceedings of the SC '24 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis, 2024. [Download, DOI:10.1109/SCW63240.2024.00009]

Y. Liu, D. Lu, Z. Zhang, F. Bao, G. Zhang, Advancing Earth System Model Calibration: A Diffusion-Based Method, Proceedings of ICLR Workshop on Tackling Climate Change with Machine Learning, 2024. [Download]

J. Yin, G. Zhang, H. Cao, S. Dash, B. Chakoumakos, F. Wang, Toward an autonomous workflow for single crystal neutron diffraction, Communications in Computer and Information Science, Vol. 1690, pp. 244-256, 2022, Springer, Cham. (DOI: 10.1007/978-3-031-23606-8_15)

H. Tran, D. Lu, and G. Zhang, Exploiting the local parabolic landscapes of adversarial losses to accelerate black-box adversarial attack, Proceedings of 17th European Conference on Computer Vision (ECCV 2022), 2022. [Download]

S. Liu, P. Zhang, D. Lu and G. Zhang, PI3NN: Out-of-distribution-aware prediction intervals from three neural networks, Proceedings of 10th International Conference on Learning Representations (ICLR), 2022. [Download]

H. Tran, D. Lu and G. Zhang, Boosting black-box adversarial attack via exploiting loss smoothness, Proceedings of ICLR Workshop on Security and Safety in Machine Learning Systems, 2021. [Download]

P. Zhang, S. Liu, D. Lu, R. Sankaran and G. Zhang, A prediction interval method for uncertainty quantification of regression models, Proceedings of ICLR Workshop on Deep Learning for Simulation, 2021. [Download]

Sirui Bi, Jiaxin Zhang and Guannan Zhang, Towards efficient uncertainty estimation in deep learning for robust energy prediction in materials chemistry, Proceedings of  ICLR Workshop on Deep Learning for Simulation, 2021. [Download]

J. Zhang, Sirui Bi, and Guannan Zhang, A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 130:3745-3753, 2021. [Download]

D. del-Castillo-Negrete, M. Yang, G. Zhang, M. Beidler, Generation and mitigation of runaway electrons: spatiotemporal effects in dynamic scenarios, Proceedings of 28th International Atomic Energy Agency (IAEA) Fusion Energy Conference, IAEA-CN-286/101, 2021. [Download]

J. Zhang, H. Tran, D. Lu, and G. Zhang,  Enabling long-range exploration in minimization of multimodal functions, Proceedings of 37th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 161: 1639-1649, 2021. [Download]

J. Zhang, S. Bi, and G. Zhang, A hybrid gradient method to designing Bayesian experiments for implicit models, Proceedings of NeurIPS  2020 Workshop on Machine Learning and the Physical Sciences, 2020. [Download]

J. Zhang, S. Bi, and G. Zhang, Scalable deep-learning-accelerated topology optimization for additively manufactured materials, Proceedings of NeurIPS 2020 Workshop on Machine Learning for Engineering Modeling, Simulation and Design, 2020.  [Download]

J. Zhang, S. Bi, and G. Zhang, A nonlocal-gradient descent method for inverse design in nanophotonics,  Proceedings of NeurIPS 2020 Workshop on Machine Learning for Engineering Modeling, Simulation and Design, 2020. [Download]

G. Zhang, J. Zhang and J. Hinkle, Learning nonlinear level sets for dimensionality reduction in function approximation, Advances in Neural Information Processing Systems (NeurIPS), 32, pp. 13199-13208, 2019. [Download]

G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster, An efficient surrogate modeling approach in Bayesian uncertainty analysis, AIP Conference Proceedings, 1558, pp. 898-901, 2013. (DOI:10.1063/1.4825643)