## Research Interests

Scientific computing, numerical analysis, and scientific machine learning.

- Machine learning moment closures for kinetic models
- Adaptive sparse grid discontinuous Galerkin methods for high-dimensional PDEs
- High-order numerical schemes for hyperbolic equations
- Boundary schemes of lattice Boltzmann method

## Google Scholar

## Preprints

32. M. Bauerle, A. J. Christlieb, M. Ding, and J. Huang. On the rotational invariance and hyperbolicity of shallow water moment equations in two dimensions, *arXiv preprint arXiv:2306.07202*, submitted, 2023.

31. A. Galindo-Olarte, J. Huang, J. Ryan, and Y. Cheng. Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations, *arXiv preprint arXiv:2210.07908*, submitted, 2022.

## Publications in Refereed Journals

30. J. Huang, W. Guo, and Y. Cheng. Adaptive sparse grid discontinuous Galerkin method: review and software implementation, *Communications on Applied Mathematics and Computation*, 2023. (Focused issue in memory of Prof. Ching-Shan Chou).

29. J. Huang, R. Li, and Y. Zhou. Coupling conditions for linear hyperbolic relaxation systems in two-scales problems, *Mathematics of Computation*, 92, 2133-2165, 2023.

28. J. Huang, T. Izgin, S. Kopecz, A. Meister, and C.-W. Shu. On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes, *ESAIM: Mathematical Modelling and Numerical Analysis (M2AN)*, 57, 1063–1086, 2023.

27. F. Zhu, J. Huang, and Y. Yang. Bound-preserving discontinuous Galerkin methods with modified Patankar time integrations for chemical reacting flows, *Communications on Applied Mathematics and Computation*, 1-28, 2023. (Focused issue in memory of Prof. Ching-Shan Chou).

26. J. Huang, Y. Cheng, A. J. Christlieb, and L. F. Roberts. Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds, *Journal of Scientific Computing*, 94(1), 1-27, 2023.

25. J. Huang, Y. Cheng, A. J. Christlieb, L. F. Roberts, and W.-A. Yong. Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, *SIAM Journal on Multiscale Modeling and Simulation*, 21(2), 489–512, 2023.

24. J. Huang, Y. Cheng, A. J. Christlieb, and L. F. Roberts. Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure, *Journal of Computational Physics*, 453, 110941, 2022.

23. J. Huang, Y. Liu, Y. Liu, Z. Tao, and Y. Cheng. A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations, *SIAM Journal on Scientific Computing*, 44(2), A745-A769, 2022.

22. J. Huang, Y. Zhou, and W.-A. Yong. Data-driven discovery of multiscale chemical reactions governed by the law of mass action, *Journal of Computational Physics*, 448, 110743, 2022.

21. J. Huang, Z. Ma, Y. Zhou, and W.-A. Yong. Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows, *Journal of Non-Equilibrium Thermodynamics*, 46 (4), 355-370, 2021.

20. W. Guo, J. Huang, Z. Tao, and Y. Cheng. An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions, *Journal of Computational Physics*, 436, 110294, 2021.

19. W. Zhao, J. Huang, and W.-A. Yong. Lattice Boltzmann method for stochastic convection-diffusion equations, *SIAM/ASA Journal on Uncertainty Quantification*, 9(2), 536-563, 2021.

18. Z. Tao, J. Huang, Y. Liu, W. Guo, and Y. Cheng. An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations, *Communications on Applied Mathematics and Computation*, 1-24, 2021. (Special issue on discontinuous Galerkin methods).

17. J. Huang, Y. Liu, W. Guo, Z. Tao, and Y. Cheng. An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form, *Journal of Scientific Computing*, 85 (13), 2020.

16. W. Zhao and J. Huang. Boundary treatment of implicit-explicit Runge-Kutta method for hyperbolic systems with source terms, *Journal of Computational Physics*, 423, 109828, 2020.

15. W. Zhao, J. Huang, and S. J. Ruuth. Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws, *Journal of Computational Physics*, 421, 109697, 2020.

14. J. Huang and Y. Cheng. An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensions, *SIAM Journal on Scientific Computing*, 42(5), A2943–A2973, 2020.

13. W. Zhao, J. Huang, and W.-A. Yong. Boundary conditions for kinetic theory based models I: lattice Boltzmann models, *SIAM Journal on Multiscale Modeling and Simulation*, 17(2), 854-872, 2019.

12. J. Huang, W. Zhao, and C.-W. Shu. A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows, *Journal of Scientific Computing*, 79, 1015-1056, 2019.

11. J. Huang and C.-W. Shu. Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows, *Journal of Scientific Computing*, 78, 1811-1839, 2019.

10. J. Huang and C.-W. Shu. Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms, *Journal of Computational Physics*, 361, 111-135, 2018.

9. J. Huang and C.-W. Shu. A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model, *Mathematical Models and Methods in Applied Sciences*, 27 (03), 549-579, 2017.

8. J. Huang and C.-W. Shu. Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, *Numerical Methods for Partial Differential Equations*, 33 (2), 467-488, 2017.

7. Z.-X. Hu, J. Huang, W.-X. Huang, and G.-X. Cui. Second-order curved interface treatments of the lattice Boltzmann method for convection-diffusion equations with conjugate interfacial conditions, *Computers and Fluids*, 144, 60-73, 2017.

6. Z. Hu, J. Huang, and W.-A. Yong. Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, *Physical Review E*, 93(4), 043320, 2016.

5. J. Huang, Z. Hu, and W.-A. Yong. Second-order curved boundary treatments of the lattice Boltzmann method for convection-diffusion equations, *Journal of Computational Physics*, 310, 26-44, 2016.

4. J. Huang, L. Hong, and W.-A. Yong. Generalization of the Kullback-Leibler divergence in the Tsallis statistics, *Journal of Mathematical Analysis and Applications*, 436(1), 501-512, 2016.

3. J. Huang and W.-A. Yong. Boundary conditions of the lattice Boltzmann method for convection-diffusion equations, *Journal of Computational Physics*, 300, 70-91, 2015.

2. J. Huang, H. Wu, and W.-A. Yong. On initial conditions for the lattice Boltzmann method, *Communications in Computational Physics*, 18(2), 450-468, 2015.

1. J. Huang, L. Zhang, W.-A. Yong, and M. Wang. On complex boundary conditions of the lattice Boltzmann method for the diffusion equations, *Applied Mathematics and Mechanics (Chinese Edition)*, 35(3), 305-312, 2014.

## Software

*AdaM-DG (Adaptive Multiresolution DG)*

I developed an adaptive multiresolution discontinuous Galerkin (DG) C++ package for solving partial differential equations in high dimensions.