Research Areas

Design algorithms for parameter-derivatives of long-time statistics of chaotic systems in engineering or physics. I devised the nonintrusive shadowing and the fast response algorithms. They are the most efficient algorithms for recursively sampling linear responses on an orbit, which works in very high dimensional chaos.

Education

2017-2021 Ph.D. Applied math, University of California, Berkeley, USA.

Adviser: John Strain.

2014-2017 M.S.E. Computational design and optimization, MIT, Cambridge, USA.

2011-2014 M.S.E. Engineering mechanics, Tsinghua University, Beijing, China.

Adviser: Haixin Chen.

2007-2011 B.E. Mechanical engineering, Tsinghua University, Beijing, China.

Research experience

2021-2023 Postdoc Beijing International Center for Mathematical Research,

Peking University, China. Mentor: Pingwen Zhang.

Publications

[1] “Adjoint shadowing for backpropagation in hyperbolic chaos”, Angxiu Ni*, https://arxiv.org/abs/2207.06648.

[2] “Divergence formulas for sampling derivatives of transfer operators on an orbit”, Angxiu Ni*, https://arxiv.org/abs/2108.13863.

[3] “Fast adjoint differentiation of chaos”, Angxiu Ni*, https://arxiv.org/abs/2111.07692.

[4] “Fast differentiation of chaos”, Angxiu Ni*, https://arxiv.org/abs/2009.00595.

[5] “Approximating linear response formula by non-intrusive shadowing algorithms”, Angxiu Ni*, SIAM J. Numer. Anal., 59(6), Pages 2843–2865, 2021.

[6] “Adjoint sensitivity analysis on chaotic dynamical systems by non-intrusive least squares adjoint shadowing (NILSAS)”, Angxiu Ni*, Chaitanya Talnikar, Journal of Computa-

tional Physics, Volume 395, Page 690-709, 15 October 2019.

[7] “Hyperbolicity, shadowing directions, and sensitivity analysis of a turbulent 3-D flow”, Angxiu Ni*, Journal of Fluid Mechanics, Volume 863, Page 644-669, 28 January 2019.

[8] “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, 1 October 2019.

[9] “Sensitivity analysis on chaotic dynamical systems by non-intrusive least squares shad-owing (NILSS)”, Angxiu Ni*, Qiqi Wang, Journal of Computational Physics, Volume 347, Page 56-77, 15 October 2017.