Zhichao Peng

Zhichao Peng

Publications

You can also find my publication record on Google Scholar. Papers (up to 10/2026) are listed below. Google scholar does a much better tracking job than myself.

Recent highlights and interest

Recent advances in low-rank numerical solvers and data-driven model order reduction offer opportunities to mitigate the curse of dimensionality in kinetic equations posed in high-dimensional phase space.

Low-rank iterative solvers for high-dimensional elliptic equations and low-rank time integrators for kinetic equations are well established, while low-rank iterative solvers for kinetic equations remain under active development. For the radiative transfer equation (RTE), we have recently developed efficient sampling-based rank-adaptation techniques compatible with the transport sweeps and synthetic acceleration methods widely used in RTE community. We further improve their efficiency via adaptive accuracy control at each iteration. (See Guo–Peng, 2026, accepted by SISC, and Han–Einkemmer–Guo–Peng, 2026, preprint.)

Inverse problems, sensitivity analysis, and uncertainty quantification often require solving the RTE for many parameter values, such as different scattering strengths or source configurations. Data-driven reduced-order models (ROMs) built from accumulated solution data can exploit low-rank structures across parameters or time steps in parametric or time-dependent RTE. Heuristically, ROMs can effectively capture dominating low-frequency structures, and classical preconditioners damp high-frequency error components faster. Building on this complementary strength, we design hybrid preconditioners for parametric RTE that combine the efficiency of data-driven ROMs with the robustness of classical diffusion synthetic acceleration (DSA). (See Peng, 2024, JCP, and Tang–Peng, 2025, preprint.)

Low-rank solvers exploit low-rank structures in the phase space of the RTE, while data-driven ROMs exploit structures across parameters but typically require high-dimensional kinetic training data. These complementary strengths motivate combining the two approaches. We have constructed data-driven low-rank ROMs directly from streaming low-rank solution data. The resulting ROMs have a cheaper offline stage than classical ROMs built from full-rank data, and their online stage is more efficient than the underlying low-rank solver. (See Guo–Peng, 2026, preprint on incremental tensor-train compression.)

Preprints

  1. C. Han, L. Einkemmer, W. Guo, Z. Peng, Low-rank SI-DSA and GMRES-DSA for Radiative Transfer Equation with Adaptive Accuracy Control, 2026. arXiv:2610.07653.

  2. D. Appelö, W. D. Henshaw, Z. Peng, Numerical Study of Eigenvector Deflation to Accelerate the WaveHoltz Method, 2026. arXiv:2606.31842.

  3. W. Guo, Z. Peng, Incremental Tensor-Train Compression from Streaming TT-Formatted Data: Applications to Reduced-Order Modeling, 2026. arXiv:2606.26900.

  4. M. Li, Y. Xiang, Z. Peng, Enhancing Future Prediction of Linear and Nonlinear Reduced-Order Models for Transport-Dominated Problems Using Lagrangian Data, 2026. arXiv:2603.19702.

  5. N. Liu, Z. Peng, On-the-Fly ROM-Based Acceleration of SI-DSA for Implicit Time Marching of the Radiative Transfer Equation, 2026. arXiv:2603.19647.

  6. N. Tang, Z. Peng, Synthetic Acceleration Preconditioners for Parametric Radiative Transfer Equations based on Trajectory-Aware Reduced Order Models, 2025. arXiv:2509.05001.

  7. A. Galindo-Olarte, Z. Peng, J. K. Ryan, Superconvergence Extraction of Upwind Discontinuous Galerkin Method Solving the Radiative Transfer Equation, 2025. arXiv:2509.00296.

  8. T. Jin, Z. Peng, Y. Xiang, Adaptive and hybrid reduced order models to mitigate Kolmogorov barrier in a multiscale kinetic transport equation, 2025. arXiv:2505.08214.

  9. Y.-M. Law, Z. Peng, D. Appelö, T. Hagstrom, A P-Adaptive Hermite Method for Nonlinear Dispersive Maxwell’s Equations, 2025. arXiv:2504.09269.

Accepted papers

  1. W. Guo, Z. Peng, Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation, accepted by SIAM Journal on Scientific Computing, 2026. arXiv:2603.25233.

Journal articles

  1. W. Guo, Z. Peng, An Inexact Low-Rank Source Iteration for Steady-State Radiative Transfer Equation with Diffusion Synthetic Acceleration, Journal of Computational Physics, article 115427, in press, 2026. Journal · arXiv:2509.00805.

  2. L. Ji, Z. Peng, Y. Chen, AAROC: Reduced Over-Collocation Method With Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations, Numerical Methods for Partial Differential Equations, 41(5), e70031, 2025. Journal · arXiv:2412.02152.

  3. Z. Peng, A flexible GMRES solver with reduced order model enhanced synthetic acceleration preconditioner for parametric radiative transfer equation, Journal of Computational Physics, 534, 114004, 2025. Journal · arXiv:2410.08735.

  4. Z. Peng, Reduced order model enhanced source iteration with synthetic acceleration for parametric radiative transfer equation, Journal of Computational Physics, 517, 113303, 2024. arXiv:2402.10488.

  5. Z. Peng, Y. Chen, Y. Cheng, F. Li, A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation, Multiscale Modeling & Simulation, 22(1), 639–666, 2024. arXiv:2211.04677.

  6. Z. Peng, D. Appelö, S. Liu, Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness, Journal of Scientific Computing, 97, article 40, 2023. arXiv:2204.06083.

  7. L. A. Martinez, Z. Peng, D. Appelö, D. M. Tennant, N. A. Petersson, J. L. DuBois, Y. J. Rosen, Noise-specific beating in the higher-level Ramsey curves of a transmon qubit, Applied Physics Letters, 122(11), 114002, 2023. Journal · arXiv:2211.06531.

  8. Z. Peng, M. Wang, F. Li, A learning-based projection method for model order reduction of transport problems, Journal of Computational and Applied Mathematics, 418, 114560, 2023. arXiv:2105.14633.

  9. H. Zhang, Z. Peng, Total generalized variation for triangulated surface data, Journal of Scientific Computing, 93, article 87, 2022.

  10. Z. Peng, D. Appelö, EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers, IEEE Transactions on Antennas and Propagation, 70(7), 2022. Journal · arXiv:2103.14789 · Short tutorial and 1D demo code.

  11. Z. Peng, Y. Chen, Y. Cheng, F. Li, A reduced basis method for radiative transfer equation, Journal of Scientific Computing, 91, article 5, 2022. arXiv:2103.07574.

  12. Z. Peng, F. Li, Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement, SIAM Journal on Scientific Computing, 43(2), A1194–A1220, 2021. arXiv:2006.07497.

  13. Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property, SIAM Journal on Numerical Analysis, 59(2), 925–954, 2021. arXiv:2005.05454.

  14. Z. Peng, Q. Tang, X.-Z. Tang, An Adaptive Discontinuous Petrov–Galerkin Method for the Grad–Shafranov Equation, SIAM Journal on Scientific Computing, 42(5), B1227–B1249, 2020. Journal · arXiv:2001.04524.

  15. Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling, Journal of Computational Physics, 415, 109485, 2020. Journal.

  16. Z. Peng, V. A. Bokil, Y. Cheng, F. Li, Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension, Journal of Computational Physics, 402, 109101, 2020. Journal.

Technical Reports

  1. Z. Peng, D. Appelö, N. A. Petersson, M. Motamed, F. Garcia, Y. Cho, Deterministic and Bayesian Characterization of Quantum Computing Devices, 2023. arXiv:2306.13747.

  2. Z. Peng, D. Appelö, N. A. Petersson, F. Garcia, Y. Cho, Mathematical approaches for characterization, control, calibration and validation of a quantum computing device, 2023. arXiv:2301.10712.