95 citations · 185 across the 15 of their papers we have counts for
15 papers
Full-window branch discovery and loss-selected EnKF continuation for data assimilation
Angxiu Ni
We develop a framework for offline full-window branch discovery, optionally followed by online continuation with an ensemble Kalman filter (EnKF). Three mechanisms drive the branch…
Ergodic and foliated kernel-differentiation method for linear responses of random systems
Angxiu Ni
We extend the kernel-differentiation method for the linear response (parameter-derivative of averaged observables) of random dynamical systems. First, for the linear response of ph…
Equivariant divergence formula for chaotic flows
Angxiu Ni, Yao Tong
We prove the equivariant divergence formula for the axiom A flow attractors, which is a recursive formula for perturbation of transfer operators of physical measures along center-u…
No-propagate algorithm for linear responses of random chaotic systems
Angxiu Ni
We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with s…
Backpropagation in hyperbolic chaos via adjoint shadowing
Angxiu Ni
To generalize the backpropagation method to both discrete-time and continuous-time hyperbolic chaos, we introduce the adjoint shadowing operator acting on covector fi…
Fast adjoint differentiation of chaos via computing unstable perturbations of transfer operators
Angxiu Ni
We devise the fast adjoint response algorithm for the gradient of physical measures (long-time-average statistics) of discrete-time hyperbolic chaos with respect to many system par…
Recursive divergence formulas for perturbing unstable transfer operators and physical measures
Angxiu Ni, Yao Tong
We show that the derivative of the (measure) transfer operator with respect to the parameter of the map is a divergence. Then, for physical measures of discrete-time hyperbolic cha…
Fast differentiation of hyperbolic chaos
Angxiu Ni
We derive and prove the `fast response' formula for the linear response, the parameter derivatives of long-time-averaged statistics, of hyperbolic deterministic chaotic systems. Th…
Approximating linear response by nonintrusive shadowing algorithms
Angxiu Ni
Nonintrusive shadowing algorithms efficiently compute , the difference between shadowing trajectories, then use to compute derivatives of averaged objectives of chaos with r…
Linear Range in Gradient Descent
Angxiu Ni, Chaitanya Talnikar
This paper defines linear range as the range of parameter perturbations which lead to approximately linear perturbations in the states of a network. We compute linear range from th…
Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
Angxiu Ni
For hyperbolic diffeomorphisms, we define adjoint shadowing directions as a bounded inhomogeneous adjoint solution whose initial condition has zero component in the unstable adjoin…
Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)
Angxiu Ni, Qiqi Wang, Pablo Fernandez +1
We present the Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS) algorithm for computing sensitivities of long-time averaged quantities in chaotic dynamical system…
Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
Angxiu Ni
This paper uses compressible flow simulation to analyze the hyperbolicity, shadowing directions, and sensitivities of a weakly turbulent three dimensional cylinder flow at Reynolds…
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)
Angxiu Ni, Qiqi Wang
This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical s…
Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs
Mario Chater, Angxiu Ni, Qiqi Wang
This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this…