Publications
2024
- C. BONNEVILLE, X. HE, A. TRAN, J. SUR PARK, W. FRIES, D. A. MESSENGER, S. WUN CHEUNG, Y. SHIN, D. M. BORTZ, D. GHOSH, J.-S. CHEN, J. BELOF and Y. CHOI, A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling, 2024, pp. arXiv:2403.10748. DOI: 10.48550/arXiv.2403.10748
- 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
- A. J. CHRISTLIEB, M. DING, J. HUANG and N. A. KRUPANSKY, Hyperbolic Machine Learning Moment Closures for the BGK Equations, 2024, pp. arXiv:2401.04783. DOI: 10.48550/arXiv.2401.04783
- A. J. CHRISTLIEB, W. A. SANDS and S. WHITE, A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition, 2024, pp. arXiv:2401.08954. DOI: 10.48550/arXiv.2401.08954
- 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, 2024, pp. arXiv:2402.13768. DOI: 10.48550/arXiv.2402.13768
- A. A. GORODETSKY, J. D. JAKEMAN and M. S. ELDRED, Grouped approximate control variate estimators, 2024, pp. arXiv:2402.14736. DOI: 10.48550/arXiv.2402.14736
- S. SCHOTTHÖFER, M. P. LAIU, M. FRANK and C. D. HAUCK, Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system, 2024, pp. arXiv:2404.14312. DOI: 10.48550/arXiv.2404.14312
- 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
- Z. MA, J. HUANG and W.-A. YONG, Uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for linear hyperbolic relaxation systems, 2023, pp. arXiv:2310.05342. DOI: 10.48550/arXiv.2310.05342
- Z. JORTI, Q. TANG, K. LIPNIKOV and X.-Z. TANG, A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions, 2023, pp. arXiv:2303.08337. DOI: 10.48550/arXiv.2303.08337
- 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, 2023, pp. arXiv:2312.05339. DOI: 10.48550/arXiv.2312.05339
- P. YIN, E. ENDEVE, C. D. HAUCK and S. R. SCHNAKE, A semi-implicit dynamical low-rank discontinuous Galerkin method for space homogeneous kinetic equations. Part I: emission and absorption, 2023, pp. arXiv:2308.05914. DOI: 10.48550/arXiv.2308.05914
- 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. A. CORRILLO, J. HU and S. Q. VAN FLEET, A particle method for the multispecies Landau equation, arXiv preprint arXiv:2310.16143 (2023). DOI:10.48550/arXiv.2310.16143
- 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
- A. J. CHRISTLIEB, W. A. SANDS and S. WHITE, A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation, 2022, pp. arXiv:2208.11291. DOI: 10.48550/arXiv.2208.11291
- 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