Publications

Publication List

2025

C. LIU, J. HU, W. T. TAITANO and X. ZHANG, An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker–Planck equations, Computers & Mathematics with Applications, 192 (2025), pp. 54-71. DOI: 10.1016/j.camwa.2025.05.008
J. HU, S. Q. VAN FLEET and A. T. S. WAN, Fully Discrete Energy-Dissipative and Conservative Discrete Gradient Particle Methods for a Class of Continuity Equations, SIAM Journal on Scientific Computing, 47 (2025), pp. A1835-A1857. DOI: 10.1137/24m1674054
D. APPELÖ and Y. CHENG, Kraus is king: High-order completely positive and trace preserving (CPTP) low rank method for the Lindblad master equation, Journal of Computational Physics, 534 (2025), pp. 114036. DOI: 10.1016/j.jcp.2025.114036
S. SCHOTTHÖFER, M. P. LAIU, M. FRANK and C. D. HAUCK, Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation, Journal of Computational Physics, 533 (2025), pp. 113967. DOI: 10.1016/j.jcp.2025.113967
N. ZHENG, D. HAYES, A. CHRISTLIEB and J.-M. QIU, A semi-Lagrangian adaptive-rank (SLAR) method for linear advection and nonlinear Vlasov-Poisson system, Journal of Computational Physics, 532 (2025), pp. 113970. DOI: 10.1016/j.jcp.2025.113970
L. CHACÓN and G. CHEN, Local conservation of energy in fully implicit PIC algorithms, Journal of Computational Physics, 529 (2025), pp. 113862. DOI: 10.1016/j.jcp.2025.113862
E. HABBERSHAW, C. D. HAUCK, J. HU and J. R. HAACK, A Nonlinear, Conservative, Entropic Fokker–Planck Model for Multi-species Collisions, Journal of Statistical Physics, 192 (2025), pp. 59. DOI: 10.1007/s10955-025-03436-7
G. VASEY, D. MESSENGER, D. BORTZ, A. CHRISTLIEB and B. O'SHEA, Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems, Journal of Computational Physics, 524 (2025), pp. 113719. DOI: 10.1016/j.jcp.2025.113719
D. APPELÖ and Y. CHENG, Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations, Journal of Scientific Computing, 102 (2025), pp. 81. DOI: 10.1007/s10915-025-02808-1
L. SEELINGER, A. REINARZ, M. B. LYKKEGAARD, R. AKERS, A. M. A. ALGHAMDI, D. ARISTOFF, W. BANGERTH, J. BÉNÉZECH, M. DIEZ, K. FREY, J. D. JAKEMAN, J. S. JØRGENSEN, K.-T. KIM, B. M. KENT, M. MARTINELLI, M. PARNO, R. PELLEGRINI, N. PETRA, N. A. B. RIIS, K. ROSENFELD, A. SERANI, L. TAMELLINI, U. VILLA, T. J. DODWELL and R. SCHEICHL, Democratizing uncertainty quantification, Journal of Computational Physics, 521 (2025), pp. 113542. DOI: 10.1016/j.jcp.2024.113542
J. W. BURBY, I. A. MALDONADO, M. RUTH, D. A. MESSENGER and L. CARBAJAL, Nonperturbative Guiding Center Model for Magnetized Plasmas, Physical Review Letters, 134 (2025), pp. 175101. DOI: 10.1103/PhysRevLett.134.175101
R. R. W. WANG and D. A. MESSENGER, Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics, Physical Review A, 111 (2025), pp. 033311. DOI: 10.1103/PhysRevA.111.033311
A. J. CHRISTLIEB, W. A. SANDS and S. R. WHITE, A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation, Journal of Scientific Computing, 103 (2025), pp. 15. DOI: 10.1007/s10915-025-02824-1
P. YIN, E. ENDEVE, C. HAUCK and S. SCHNAKE, Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model, Mathematics of Computation, 94 (2025), pp. 1199-1233.
A. C. K. P. Z. T. S. W. B. W. S. M. WISE, Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow, Communications in Computational Physics, 37 (2025), pp. 877-920. DOI: doi:10.4208/cicp.OA-2023-0190
J. NAKAO, J.-M. QIU and L. EINKEMMER, Reduced Augmentation Implicit Low-Rank (RAIL) Integrators for Advection-Diffusion and Fokker–Planck Models, SIAM Journal on Scientific Computing, 47 (2025), pp. A1145-A1169. DOI: 10.1137/23m1622921
X. HE, A. TRAN, D. M. BORTZ and Y. CHOI, Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification, International Journal for Numerical Methods in Engineering, 126 (2025), pp. e7634. DOI: 10.1002/nme.7634
A. J. CHRISTLIEB, M. DING, J. HUANG and N. A. KRUPANSKY, Hyperbolic Machine Learning Moment Closures for the BGK Equations, Multiscale Modeling & Simulation, 23 (2025), pp. 187-217. DOI: 10.1137/24m1629377
M. BAUERLE, A. J. CHRISTLIEB, M. DING and J. HUANG, On the Rotational Invariance and Hyperbolicity of Shallow Water Moment Equations in Two Dimensions, SIAM Journal on Mathematical Analysis, 57 (2025), pp. 1039-1085. DOI: 10.1137/23m1579789

2024

D. MESSENGER, A. TRAN, V. DUKIC and D. BORTZ, The Weak Form is Stronger Than You Think, SIAM News, 57 (2024).
S.-Y. CHO, M. GROPPI, J.-M. QIU, G. RUSSO and S.-B. YUN, Conservative Semi-Lagrangian Methods for Kinetic Equations, in J. A. Carrillo and E. Tadmor, eds., Active Particles, Volume 4: Theory, Models, Applications, Springer Nature Switzerland, Cham, 2024, pp. 283-420.
H. EL KAHZA, W. TAITANO, J.-M. QIU and L. CHACÓN, Krylov-based adaptive-rank implicit time integrators for stiff problems with application to nonlinear Fokker-Planck kinetic models, Journal of Computational Physics, 518 (2024), pp. 113332. DOI: 10.1016/j.jcp.2024.113332
J. CHEN, J. NAKAO, J.-M. QIU and Y. YANG, A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws, Journal of Scientific Computing, 102 (2024), pp. 12. DOI: 10.1007/s10915-024-02714-y
A. J. CHRISTLIEB, W. A. SANDS and S. R. WHITE, A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition, Journal of Scientific Computing, 101 (2024), pp. 73. DOI: 10.1007/s10915-024-02728-6
B. YE, J. HU, C.-W. SHU and X. ZHONG, Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system with Dougherty-Fokker-Planck collision operator, Journal of Computational Physics, 514 (2024), pp. 113219. DOI: 10.1016/j.jcp.2024.113219
M. DING, J.-M. QIU and R. SHU, Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model, Advances in Computational Science and Engineering, 2 (2024), pp. 222-245. DOI: 10.3934/acse.2024012
B. P. RUSSO, D. A. MESSENGER, D. BORTZ and J. A. ROSENFELD, Weighted Composition Operators for Learning Nonlinear Dynamics, IFAC-PapersOnLine, 58 (2024), pp. 97-102. DOI: 10.1016/j.ifacol.2024.10.120
D. MESSENGER, G. DWYER and V. DUKIC, Weak-form inference for hybrid dynamical systems in ecology, Journal of The Royal Society Interface, 21 (2024), pp. 20240376. DOI: doi:10.1098/rsif.2024.0376
D. A. MESSENGER and D. M. BORTZ, Asymptotic consistency of the WSINDy algorithm in the limit of continuum data, IMA Journal of Numerical Analysis (2024). DOI: 10.1093/imanum/drae086
X. XIE, Q. TANG and X. TANG, Latent space dynamics learning for stiff collisional-radiative models, Machine Learning: Science and Technology, 5 (2024), pp. 045070. DOI: 10.1088/2632-2153/ad9ce7
J. A. CARRILLO, J. HU and S. Q. VAN FLEET, A Particle Method for the Multispecies Landau Equation, Acta Applicandae Mathematicae, 194 (2024), pp. 6. DOI: 10.1007/s10440-024-00692-9
R. BAILO, J. A. CARRILLO and J. HU, The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations, Journal of Plasma Physics, 90 (2024). DOI: 10.1017/S0022377824001077.
D. A. MESSENGER, J. W. BURBY and D. M. BORTZ, Coarse-graining Hamiltonian systems using WSINDy, Scientific Reports, 14 (2024), pp. 14457. DOI: 10.1038/s41598-024-64730-0
J. HU, A. JÜNGEL and N. ZAMPONI, Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system, Kinetic and Related Models, 17 (2024), pp. 939-970. DOI: 10.3934/krm.2024007
L. F. RICKETSON and L. CHACÓN, Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields, Journal of Computational Physics, 513 (2024), pp. 113136. DOI: 10.1016/j.jcp.2024.113136
J. S. R. PARK, S. W. CHEUNG, Y. CHOI and Y. SHIN, tLaSDI: Thermodynamics-informed latent space dynamics identification, Computer Methods in Applied Mechanics and Engineering, 429 (2024), pp. 117144. DOI: 10.1016/j.cma.2024.117144
S. SCHNAKE, C. KENDRICK, E. ENDEVE, M. STOYANOV, S. HAHN, C. D. HAUCK, D. L. GREEN, P. SNYDER and J. CANIK, Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model, Journal of Computational Physics, 510 (2024), pp. 113053. DOI: 10.1016/j.jcp.2024.113053
J. COUGHLIN, J. HU and U. SHUMLAK, Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition, Journal of Computational Physics, 509 (2024), pp. 113055. DOI: 10.1016/j.jcp.2024.113055
T. KADEETHUM, D. O’MALLEY, Y. CHOI, H. S. VISWANATHAN and H. YOON, Progressive transfer learning for advancing machine learning-based reduced-order modeling, Scientific Reports, 14 (2024), pp. 15731. DOI: 10.1038/s41598-024-64778-y
A. TRAN, X. HE, D. A. MESSENGER, Y. CHOI and D. M. BORTZ, Weak-form latent space dynamics identification, Computer Methods in Applied Mechanics and Engineering, 427 (2024), pp. 116998. DOI: 10.1016/j.cma.2024.116998
Y. KIM, Y. CHOI and B. YOO, Gappy AE: A nonlinear approach for Gappy data reconstruction using auto-encoder, Computer Methods in Applied Mechanics and Engineering, 426 (2024), pp. 116978. DOI: 10.1016/j.cma.2024.116978
A. N. DIAZ, Y. CHOI and M. HEINKENSCHLOSS, A fast and accurate domain decomposition nonlinear manifold reduced order model, Computer Methods in Applied Mechanics and Engineering, 425 (2024), pp. 116943. DOI: 10.1016/j.cma.2024.116943
M. J. PICKLO, Q. TANG, Y. ZHANG, J. K. RYAN and X.-Z. TANG, Denoising Particle-In-Cell data via Smoothness-Increasing Accuracy-Conserving filters with application to Bohm speed computation, Journal of Computational Physics, 502 (2024), pp. 112790. DOI: 10.1016/j.jcp.2024.112790
N. CHENG, O. A. MALIK, S. DE, S. BECKER and A. DOOSTAN, Bi-fidelity variational auto-encoder for uncertainty quantification, Computer Methods in Applied Mechanics and Engineering, 421 (2024), pp. 116793. DOI: 10.1016/j.cma.2024.116793
J. HUANG, W. GUO and Y. CHENG, Adaptive Sparse Grid Discontinuous Galerkin Method: Review and Software Implementation, Communications on Applied Mathematics and Computation, 6 (2024), pp. 501-532. DOI: 10.1007/s42967-023-00268-8
W. GUO, J. F. EMA and J.-M. QIU, A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics, Communications on Applied Mathematics and Computation, 6 (2024), pp. 550-575. DOI: 10.1007/s42967-023-00277-7
B. BURNETT, S. GOTTLIEB and Z. J. GRANT, Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods, Communications on Applied Mathematics and Computation, 6 (2024), pp. 705-738. DOI: 10.1007/s42967-023-00315-4
X. HONG and J.-M. QIU, A Conservative Eulerian–Lagrangian Runge–Kutta Discontinuous Galerkin Method for Linear Hyperbolic System with Large Time Stepping, Journal of Scientific Computing, 98 (2024), pp. 70. DOI: 10.1007/s10915-024-02452-1
K. DOHERTY, C. SIMPSON, S. BECKER and A. DOOSTAN, QuadConv: Quadrature-based convolutions with applications to non-uniform PDE data compression, Journal of Computational Physics, 498 (2024), pp. 112636. DOI: 10.1016/j.jcp.2023.112636
D. M. BORTZ, D. A. MESSENGER and A. TRAN, Chapter 2 - Weak form-based data-driven modeling: Computationally efficient and noise robust equation learning and parameter inference, in S. Mishra and A. Townsend, eds., Handbook of Numerical Analysis, Elsevier, 2024, pp. 53-82.
C. BONNEVILLE, Y. CHOI, D. GHOSH and J. L. BELOF, GPLaSDI: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder, Computer Methods in Applied Mechanics and Engineering, 418 (2024), pp. 116535. DOI: 10.1016/j.cma.2023.116535
J. ROSEMEIER, T. HAUT and B. WINGATE, Multilevel Parareal Algorithm with Averaging for Oscillatory Problems, SIAM Journal on Scientific Computing, 46 (2024), pp. A2709-A2736. DOI: 10.1137/23m1547123
B. W. REUTER, G. GERACI and T. WILDEY, ANALYSIS OF THE CHALLENGES IN DEVELOPING SAMPLE-BASED MULTIFIDELITY ESTIMATORS FOR NONDETERMINISTIC MODELS, International Journal for Uncertainty Quantification, 14 (2024).DOI: 10.1615/Int.J.UncertaintyQuantification.2024050125
Z. PENG, Y. CHEN, Y. CHENG and F. LI, A Micro-Macro Decomposed Reduced Basis Method for the Time-Dependent Radiative Transfer Equation, Multiscale Modeling & Simulation, 22 (2024), pp. 639-666. DOI: 10.1137/22m1533487
J. HU and R. SHU, Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation, Mathematics of Computation (2024).DOI: 10.1090/mcom/3967
L. EINKEMMER, J. HU and J. KUSCH, Asymptotic-Preserving and Energy Stable Dynamical Low-Rank Approximation, SIAM Journal on Numerical Analysis, 62 (2024), pp. 73-92. DOI: 10.1137/23m1547603
N. CHENG, O. A. MALIK, Y. XU, S. BECKER, A. DOOSTAN and A. NARAYAN, Subsampling of Parametric Models with Bifidelity Boosting, SIAM/ASA Journal on Uncertainty Quantification, 12 (2024), pp. 213-241. DOI: 10.1137/22m1524989
W. GUO and J.-M. QIU, A Conservative Low Rank Tensor Method for the Vlasov Dynamics, SIAM Journal on Scientific Computing, 46 (2024), pp. A232-A263. DOI: 10.1137/22m1473960

2023

A. J. CHRISTLIEB, W. A. SANDS and H. YANG, Order enhanced finite volume methods through non-polynomial approximation, Journal of Computational Physics, 478 (2023), pp. 111960. DOI: 10.1016/j.jcp.2023.111960
A. CHRISTLIEB, M. LINK, H. YANG and R. CHANG, High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation, Communications on Applied Mathematics and Computation, 5 (2023), pp. 116-142. DOI: 10.1007/s42967-021-00150-5
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, Multiscale Modeling & Simulation, 21 (2023), pp. 489-512. DOI: 10.1137/21m1423956.
G. CHEN and L. CHACÓN, An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields, Journal of Computational Physics, 487 (2023), pp. 112160. DOI: 10.1016/j.jcp.2023.112160.
M. DING, J.-M. QIU and R. SHU, Accuracy and Stability Analysis of the Semi-Lagrangian Method for Stiff Hyperbolic Relaxation Systems and Kinetic BGK Model, Multiscale Modeling & Simulation, 21 (2023), pp. 143-167. DOI: 10.1137/21m141871x.
D. M. BORTZ, D. A. MESSENGER and V. DUKIC, Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics, Bulletin of Mathematical Biology, 85 (2023), pp. 110. DOI: 10.1007/s11538-023-01208-6
X. HE, Y. CHOI, W. D. FRIES, J. L. BELOF and J.-S. CHEN, gLaSDI: Parametric physics-informed greedy latent space dynamics identification, Journal of Computational Physics, 489 (2023), pp. 112267. DOI: 10.1016/j.jcp.2023.112267
L. LYU and H. LEI, Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory, Physical Review Letters, 131 (2023), pp. 177301. DOI: 10.1103/PhysRevLett.131.177301
S. SCHOTTHÖFER, Synergies between Numerical Methods for Kinetic Equations and Neural Networks, Karlsruher Institut für Technologie (KIT), 2023. DOI: 10.5445/ir/1000158838
C. D. HAUCK and S. SCHNAKE, A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations, SIAM Journal on Matrix Analysis and Applications, 44 (2023), pp. 971-1005. DOI: 10.1137/22m1519493

2022

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 (2022), pp. 110941. DOI: 10.1016/j.jcp.2022.110941
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 (2022), pp. 7. DOI: 10.1007/s10915-022-02056-7
O. A. MALIK, Y. XU, N. CHENG, S. BECKER, A. DOOSTAN and A. NARAYAN, Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems, 2022, pp. arXiv:2209.05662. DOI: 10.48550/arXiv.2209.05662
Z. PENG, Y. CHEN, Y. CHENG and F. LI, A Reduced Basis Method for Radiative Transfer Equation, Journal of Scientific Computing, 91 (2022), pp. 5. DOI: 10.1007/s10915-022-01782-2