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Published and accepted
  1. 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, accepted.
  2. 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.
  3. 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), pp. 108247, 2020.
  4. 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.
  5. X. Xie, G. Zhang and C. Webster, Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network, Mathematics, 7(8), pp. 757, 2019.
  6. 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.
  7. 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.
  8. 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 (2018), pp. 062507.
  9. 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 (2018), pp. 237-258. [PDF, bibtex]
  10. 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 (2017), pp. 10802-10823. [PDF, bibtex]
  11. H. Tran, C. Webster and G. Zhang, Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients, Numerishe Mathematik, 137 (2017), pp. 451-493. [PDF, bibtex]
  12. G. Zhang, and D. del-Castillo-Negrete, A backward Monte-Carlo method for time-dependent runaway electron simulations, Physics of Plasmas, 24 (2017), pp. 092511. [PDF, bibtex]
  13. 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 (2017), pp. 213-244. [PDF, bibtex]
  14. 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 (2017), pp. 746-770. [PDF, bibtex]
  15. 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 (2017), pp. 456-466. [PDF, bibtex]
  16. 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 (2016), pp. 9642-9660. [PDF, bibtex]
  17. 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 (2016), pp. 125149. [PDF, bibtex]
  18. 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 (2016), pp. 1111-1137. [PDF, bibtex]
  19. G. Zhang, C. Webster, M. Gunzburger and J. Burkardt, Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection, SIAM Review, 58 (2016), pp. 517-551. [PDF, bibtex]
  20. F. Bao, Y. Cao, C. Webster and G. Zhang, An efficient meshfree implicit filter for nonlinear filtering problems, International Journal for Uncertainty Quantification, 6 (2016), pp. 19-33. [PDF, bibtex]
  21. 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 (2016), pp. 2479-2496. [PDF, bibtex]
  22. 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 (2016), pp. 291-313. [PDF, bibtex]
  23. 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 (2016), pp. 2231-2256. [PDF, bibtex]
  24. 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 (2015), pp. 1508-1536. [PDF, bibtex]
  25. M. Gunzburger, C. Webster and G. Zhang, Sparse collocation methods for stochastic interpolation and quadrature, Handbook of Uncertainty Quantification, pp. 1-46, Springer International Publishing, Switzerland, 2016. [PDF, bibtex]
  26. V. Reshniak, A. Khaliq, D. Voss and G. Zhang, Split-step Milstein methods for multi-channel stiff stochastic differential systems, Applied Numerical Mathematics, 89 (2015), pp. 1-23. [PDF, bibtex]
  27. 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 (2014), pp. 784-804. [PDF, bibtex]
  28. M. Gunzburger, C. Webster and G. Zhang, Stochastic finite element methods for partial differential equations with random input data, Acta Numerica, 23 (2014), pp. 521-650. [PDF, bibtex]
  29. 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 (2014), pp. 798-817. [PDF, bibtex]
  30. 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 (2014), pp. 1-15. [PDF, bibtex]
  31. 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 (2014), pp. 137-170. [PDF, bibtex]
  32. G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster, An efficient surrogate modeling approach in Bayesian uncertainty analysis, AIP Conference Proceedings, 1558 (2013), pp. 898-901. [PDF, bibtex]
  33. 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 (2013), pp. 6871-6892. [PDF,  bibtex]
  34. G. Zhang, M. Gunzburger and W. Zhao, A sparse-grid method for multi-dimensional backward stochastic differential equations, Journal of Computational Mathematics, 31 (2013), pp. 221-248. [PDF, bibtex]
  35. 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 (2012), pp. 1922-1940. [PDF, bibtex]
  36. 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 (2012), pp. 1585-1603. [PDF, bibtex]
  37. W. Zhao, G. Zhang and L. Ju, A stable multi-step scheme for solving backward stochastic differential equations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 1369-1394. [PDF, bibtex]

In progress
  1. J. Zhang, H. Tran, and G. Zhang, Accelerating Reinforcement Learning with a Directional-Gaussian-Smoothing Evolution Strategy, submitted. (https://arxiv.org/abs/2002.09077)
  2. J. Zhang, H. Tran, D. Lu, and G. Zhang, A scalable envolution strategy with directional Gaussian smoothing for blackbox optimization, submitted. (https://arxiv.org/abs/2002.03001)
  3. M. Stoyanov and G. Zhang, A multilevel reduced-basis method for parameterized partial differential equations, SIAM Journal on Scientific Comptuing, submitted.
  4. G. Zhang and D. del-Castillo-Negrete, An improved backward Monte-Carlo method for runaway electron simulations with time-dependent electrical fields, preprint.
  5. G. Zhang and D. del-Castillo-Negrete, A probabilistic adaptive semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation, submitted.