Publications
Journal publications and preprints
- "Ergodic and foliated kernel-differentiation method for linear responses of random systems",
Angxiu Ni,
Arxiv link.
- "Equivariant divergence formula for differentiating chaotic flows",
Angxiu Ni, Yao Tong, J Stat Phys 191, 118 (2024).
Journal link
Arxiv link.
- "Adjoint shadowing for backpropagation in hyperbolic chaos",
Angxiu Ni, 2024 Nonlinearity 37 035009.
Journal link
Arxiv link.
- "Recursive divergence formulas for perturbing unstable transfer operators and physical measures",
Angxiu Ni, Yao Tong, J Stat Phys 190, 126 (2023).
Journal link,
Arxiv link.
- "Fast adjoint algorithm for linear responses of hyperbolic chaos",
Angxiu Ni, SIAM Journal on Applied Dynamical Systems, 22:2792–2824, 12 2023.
Arxiv link.
(A prototype code of fast adjoint response is on GitHub.)
- "Fast differentiation of chaos",
Angxiu Ni,
Arxiv link.
(A prototype code of fast response is on GitHub.)
- "Approximating linear response by nonintrusive shadowing algorithms",
Angxiu Ni, SIAM J. Numer. Anal., 59(6), Pages 2843-2865, 2021.
Journal link,
Arxiv link.
- "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.)
- "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.)
- "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.
- "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.)
- "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.
- "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.
- "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.
Misc. Publications
- "No-propagate algorithm for linear responses of random chaotic systems",
Angxiu Ni,
Arxiv link.
This unpublished draft is superseded by the above paper "ergodic and foliated ... sytems".
- "Adjoint shadowing directions in hyperbolic systems for sensitivity analysis",
Angxiu Ni, Arxiv link.
This unpublished draft is superseded by the above paper "Adjoint shadowing ... chaos".
- "Linear range in gradient descent",
Angxiu Ni, Chaitanya Talnikar,
Arxiv link.
- "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.)
The corresponding author(s) are marked by * when applicable.
My Google Scholar Page.