Publications

This is my Google Scholar Page.
Arxiv versions may be more updated than journal versions.
The corresponding author(s) are marked by * when applicable.

    Computing linear response

  1. "Fast linear response algorithm for differentiating stationary measure of chaos",
    Angxiu Ni, Arxiv link.
    (A prototype code of linear response algorithm is on GitHub.)
    (This is a video recording of a talk on this paper, and the pdf of writing to accompensate the video quality.)
  2. "Approximating linear response formula by non-intrusive shadowing algorithms",
    Angxiu Ni, Arxiv link.

    General optimization

  3. "Linear range in gradient descent",
    Angxiu Ni, Chaitanya Talnikar, Arxiv link.

    Adjoint shadowing lemma and NILSAS

  4. "Adjoint shadowing directions in hyperbolic systems for sensitivity analysis",
    Angxiu Ni, Arxiv link.
  5. "Adjoint sensitivity analysis on chaotic dynamical systems by non-intrusive least squares adjoint shadowing (NILSAS)",
    Angxiu Ni*, Chaitanya Talnikar, Journal of Computational Physics, Volume 395, Pages 690-709, 2019, Journal link, Arxiv link.
    (A prototype code of NILSAS is on GitHub.)

    Non-intrusive shadowing

  6. "Hyperbolicity, shadowing directions, and sensitivity analysis of a turbulent 3-D flow",
    Angxiu Ni, Journal of Fluid Mechanics, Volume 863, Page 644-669, 2019, Journal link, Arxiv link.
    (Here are some YouTube videos of the CLVs and shadowing directions computed in this paper.)
  7. "Sensitivity analysis on chaotic dynamical systems by finite difference non-intrusive least squares shadowing (FD-NILSS)",
    Angxiu Ni*, Qiqi Wang, Pablo Fernandez, Chaitanya Talnikar, Journal of Computational Physics, Volume 394, Pages 615-631, 2019, Journal link, Arxiv link.
  8. "Sensitivity analysis on chaotic dynamical systems by non-intrusive least squares shadowing (NILSS)",
    Angxiu Ni*, Qiqi Wang, Journal of Computational Physics, Volume 347, Page 56-77, 2017, Journal link, Arxiv link.
    (A prototype code of NILSS is on GitHub.)

    Misc. Publications

  9. "Sensitivity analysis on chaotic dynamical system by non-intrusive least square shadowing (NI-LSS)",
    Angxiu Ni, Patrick J. Blonigan, Mario Chater, Qiqi Wang, and Zhichao Zhang, 46th AIAA fluid dynamics conference, (AIAA 2016-4399), Journal link.
    (This paper is the first public appearance of the NILSS algorithm.)
  10. "Simplified least squares shadowing sensitivity analysis for chaotic ODEs and PDEs",
    Mario Chater, Angxiu Ni, Qiqi Wang, Journal of Computational Physics 329, 126-140, 2017.
  11. "Least squares shadowing method for sensitivity analysis of differential equations",
    Mario Chater, Angxiu Ni, Patrick Blonigan, Qiqi Wang, SIAM J. Numer. Anal., 55(6), 3030–3046.
  12. "An improvement to NSGA-II algorithm and its application in optimization design of multi-element airfoil",
    Angxiu Ni, Yufei Zhang, Haixin Chen, Acta Aerodynamica Sinica 32 (2), 252-257, 2014.

Talks

  1. "Fast Linear Response Algorithm for Differentiating Stationary Measure of Chaos",
    Mathematical Physics and Dynamical Systems Seminar, UC Riverside, June 8th, 2021, hosted by Michel L. Lapidus.
  2. "Adjoint shadowing lemma for computing gradients of chaos via back-propagation",
    SIAM conference on applications of dynamical systems (DS21), May 2021, online.
  3. "Fast Linear Response Algorithm for Differentiating Stationary Measure of Chaos",
    Dynamical systems seminar, Peking University, Mar 18, 2021, online.
  4. "Fast Linear Response Algorithm for Differentiating Stationary Measure of Chaos",
    SIAM conference on computational science and engineering (CSE21), Mar 2, 2021, online.
  5. "Differentiation of conditional SRB measures for maps and flows",
    Dynamics student seminar, Feb 18, 2021, Penn state University.
  6. "Fast Linear Response Algorithm for Differentiating Stationary Measure of Chaos",
    Student Probability/PDE Seminar, Feb 12, 2021, UC Berkeley, US, hosted by Fraydoun Rezakhanlou.
  7. "Linear response algorithm for differentiating SRB measures",
    Dynamical systems seminar, Dec 09, 2020, University of Loughborough, UK, hosted by Wael Bahsoun.
  8. "Linear response algorithm for differentiating SRB measures",
    Harmonic analysis and differential equations seminar, Oct 27, 2020, UC Berkeley.
    This is the video recording, also the pdf of writing to accompensate the poor video quality.
  9. "Expanding unstable divergence",
    Dynamics student seminar, Sep 24, 2020, Penn state University.
  10. "Shadowing algorithms and linear response formula",
    Dynamics student seminar, Sep 17, 2020, Penn state University.
  11. "Towards sensitivity analysis on turbulence via shadowing methods",
    Center for turbulence research tea seminar, May 24, 2019, Stanford University, hosted by Parviz Moin.
  12. "Adjoint shadowing directions in chaotic dynamical systems for sensitivity analysis",
    SIAM conference on applications of dynamical systems (DS19), May 2019, Snowbird, Utah, U.S.
  13. "Adjoint sensitivity analysis of chaotic dynamical systems via shadowing methods",
    Applied Mathematics Seminar, Feb 7, 2019, UC Berkeley, hosted by Lin Lin.
  14. "NILSAS: adjoint sensitivity analysis for chaos via computing adjoint shadowing directions",
    SIAM conference on computational science and engineering (CSE19), Feb 2019, Spokane, Washington, USA.
  15. "Characteristic Lyapunov vectors and the shadowing direction of a 3-D cylinder flow at Reynolds number 525",
    70th annual meeting of the APS division of fluid dynamics,  Nov 2017, Denver, Colorado, USA.
  16. "Computation of sensitivity and stability in chaotic flow by non-intrusive least squares shadowing (NILSS)",
    SIAM annual meeting, Jul 2017, Pittsburgh, Pennsylvania, USA.
  17. "Sensitivity analysis on chaotic dynamical systems by non-intrusive least squares shadowing (NILSS), and challenges",
    National institute of aerospace, Jun 14, 2017, hosted by Boris Diskin and Eric Nielsen.
    (There is a good video recording of this talk, thanks to Boris and Eric.)
  18. "Sensitivity analysis on chaotic dynamical systems by non-intrusive least squares shadowing (NILSS)",
    2017 SIAM conference on computational science and engineering, Feb 2017, Atlanta, Georgia, USA.
  19. "Sensitivity analysis for chaotic dynamical systems using non-intrusive least square shadowing",
    2016 SIAM annual meeting, Jul 2016, Boston, Massachusetts, USA.
  20. "Sensitivity analysis for chaotic aeroelastic oscillations using non-intrusive least square shadowing",
    16th AIAA aviation, Jun 2016, Washington, D.C., USA.
  21. "Dynamical behaviors of a thin plate under bypassing flow",
    68th annual meeting of the APS division of fluid dynamics, Nov 2015, Boston, USA.