Significant progress has been made in multidisciplinary design optimization (MDO) research with broad applications. Currently, the partial differential equation (PDE)-constrained optimization problems with millions of state variables and thousands of design variables are solved routinely. However, from the perspective of dynamical systems, most of the previous research is focused on steady-state fixed point problems. In this seminar, we discuss efforts to extend MDO to problems categorized as bifurcation and limit cycle oscillation (LCO) with applications in aeroelasticity and fluid dynamics. Besides, research on the deep learning-based surrogate model will be presented.

Two methods are used to compute the derivatives for gradient-based optimization: the adjoint method and the algorithmic differentiation (AD). We propose novel adjoint equations for LCO and bifurcation with efficient solution methods leveraging the special structure of the equations. We present a method to derive the reverse-mode AD (RAD). A newly found RAD eigenvalue derivative formula is presented.