514 citations · 1.7k across the 51 of their papers we have counts for
52 papers
Approximating linear response of physical chaos
Adam A. Sliwiak, Qiqi Wang
Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computa…
Assessment of Detached Eddy Simulation and Sliding Mesh Interface in Predicting Tiltrotor Performance in Helicopter and Airplane Modes
Feilin Jia, John Moore, Qiqi Wang
This paper presents numerical investigation on performance and flow field of the full-scale XV-15 tiltrotor in both helicopter mode (hovering flight and forward flight) and aeropla…
Scheduled Relaxation Jacobi schemes for non-elliptic partial differential equations
Mohammad Shafaet Islam, Qiqi Wang
The Scheduled Relaxation Jacobi (SRJ) method is a linear solver algorithm which greatly improves the convergence of the Jacobi iteration through the use of judiciously chosen relax…
Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension
Adam A. Sliwiak, Qiqi Wang
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory…
Aerodynamic Risk Assessment using Parametric, Three-Dimensional Unstructured, High-Fidelity CFD and Adaptive Sampling
Runda Ji, Qiqi Wang
We demonstrate an adaptive sampling approach for computing the probability of a rare event for a set of three-dimensional airplane geometries under various flight conditions. We de…
A trajectory-driven algorithm for differentiating SRB measures on unstable manifolds
Adam A. Sliwiak, Qiqi Wang
SRB measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on…
Differentiating densities on smooth manifolds
Adam A. Sliwiak, Qiqi Wang
Lebesgue integration of derivatives of strongly-oscillatory functions is a recurring challenge in computational science and engineering. Integration by parts is an effective remedy…
Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds
Nisha Chandramoorthy, Qiqi Wang
This paper presents the space-split sensitivity or the S3 algorithm to transform Ruelle's linear response formula into a well-conditioned ergodic-averaging computation. We prove a…
Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems
Adam A. Sliwiak, Nisha Chandramoorthy, Qiqi Wang
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and th…
Adjoint-based trailing edge shape optimization of a transonic turbine vane using large eddy simulations
Chaitanya Talnikar, Qiqi Wang
The shape of the trailing edge of a gas turbine nozzle guide vane has a significant effect on the downstream stagnation pressure loss and heat transfer over the surface of the vane…
On the probability of finding a nonphysical solution through shadowing
Nisha Chandramoorthy, Qiqi Wang
This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a smal…
Variational optimization and data assimilation in chaotic time-delayed systems with automatic-differentiated shadowing sensitivity
Nisha Chandramoorthy, Luca Magri, Qiqi Wang
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differe…
A data driven heuristic for rapid convergence of Scheduled Relaxation Jacobi schemes
Mohammad Shafaet Islam, Qiqi Wang
The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high performance linear solver for elliptic partial differential equations (PDEs). The method greatly improv…
Ergodic Sensitivity Analysis of One-Dimensional Chaotic Maps
Adam A. Sliwiak, Nisha Chandramoorthy, Qiqi Wang
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach,…
An ergodic averaging method to differentiate covariant Lyapunov vectors
Nisha Chandramoorthy, Qiqi Wang
Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms to c…
Hierarchical Jacobi Iteration for Structured Matrices on GPUs using Shared Memory
Mohammad Shafaet Islam, Qiqi Wang
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial different…
A computable realization of Ruelle's formula for linear response of statistics in chaotic systems
Nisha Chandramoorthy, Qiqi Wang
We present a computable reformulation of Ruelle's linear response formula for chaotic systems. The new formula, called Space-Split Sensitivity or S3, achieves an error convergence…
Sensitivity computation of statistically stationary quantities in turbulent flows
Nisha Chandramoorthy, Qiqi Wang
It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not s…
Toward computing sensitivities of average quantities in turbulent flows
Nisha Chandramoorthy, Zhong-Nan Wang, Qiqi Wang +1
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoi…
Feasibility analysis of ensemble sensitivity computation in turbulent flows
Nisha Chandramoorthy, Pablo Fernandez, Chaitanya Talnikar +1
In chaotic systems, such as turbulent flows, the solutions to tangent and adjoint equations exhibit an unbounded growth in their norms. This behavior renders the instantaneous tang…
Nanophotonic Media for Artificial Neural Inference
Erfan Khoram, Ang Chen, Dianjing Liu +4
We show optical waves passing through a nanophotonic medium can perform artificial neural computing. Complex information, is encoded in the wave front of an input light. The medium…
RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
Jin-Long Wu, Heng Xiao, Rui Sun +1
Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linea…
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…
Multiple Shooting Shadowing for Sensitivity Analysis of Chaotic Dynamical Systems
Patrick J. Blonigan, Qiqi Wang
Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent…