OPtimization Toolkit for Highly NOn-linear Systems (OPTHiNOS)

The OPTHiNOS is a scientific software for Sensitivity Analysis (SA), Uncertainty Quantification (UQ), and optimization of large-scale chaotic dynamical systems. This novel approach leverages machine learning techniques associated with novel algorithms developed from high-level mathematical approaches. The OPTHiNOS works based on the shadowing lemma, a well-known theorem in the dynamical system studies, coupled with non-linear model reduction, which is featured by the minimum residual property.

Recent Findings

Highlighted Work

Sensitivity analysis of chaotic dynamical systems

Conventional sensitivity analysis

Conventional sensitivity analysis of chaotic dynamical systems usually fail due to strong non-linearity in the corresponding governing equations.

Present sensitivity analysis

The OPHTiNOS can efficiently compute the sensitivity solutions within a reasonable uncertainty range. It also reduces the computational memory usage up to 4,000 times than conventional approaches.

PDE-constrained optimization in the presence of massive flow separations

NACA 0012 at AOA=25 degrees.

A NACA 0012 was considered as a baseline design at AOA=25 degrees. The effort was made to reduce the drag force, while the lift force remains constant.

Optimized airfoil at AOA=25 degrees.

The optimized airfoil by the OPTHiNOS can have about 30% less drag force with almost the lift force generation.

"Stability" vs "Instability" for simple dynamical systems

Instability in conventional methods

Direct solution of the sensitivity function via explicit schemes are highly sensitive to numerical errors, and hence, the sensitivity simulations usually crash.

Stability by the OPTHiNOS

The OPTHiNOS converts initial value problems into the boundary value problems, which guarantees the stability of the sensitivity simulations.

Unsteady aerodynamic optimization of flapping wings

Fluid-Structure Interaction (FSI) problems

One of well-known FSI problems is birds flying at which complex flow structures are created due to the dynamic stall phenomenon. This problem is called challenging since the flow is highly unstable in the wake of the wings.

Unsteady flow physics in the OPTHiNOS

The OPTHiNOS can effectively handle complex optimization problems for flapping wing problems. Here, the thrust is increased, while the lift force remains unchanged to keep the balance with the bird's weight.