A new two-stage stochastic partial differential equation (PDE)-constrained optimization methodology is developed for the active vibration control of structures in the presence of uncertainties in mechanical loads. The methodology relies on the two-stage stochastic optimization formulation with an embedded first-order black-box PDEconstrained optimization procedure. The PDE-constrained optimizat...

Seismic waveform inversion aims at obtaining detailed estimates of subsurface medium parameters, such as the spatial distribution of soundspeed, from multi-experiment seismic data. A formulation of this inverse problem in the frequency-domain leads to an optimization problem constrained by a Helmholtz equation with many right-hand-sides. Application of this technique to industry-scale problem f...

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a syst...

Abstract In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where particularly focus on polymer flooding. The computational approach is based adaptive training procedure a neural network that directly approximates input-output map the underlying PDE-constrained problem. process thereby focuses construction accur...

We develop a class of V-cycle type multilevel restricted additive Schwarz (RAS) methods and study the numerical and parallel performance of the new fully coupled methods for solving large sparse Jacobian systems arising from the discretization of some optimization problems constrained by nonlinear partial differential equations. Straightforward extensions of the one-level RAS to multilevel do n...

We introduce a technique for the dimension reduction of a class of PDE constrained optimization problems governed by linear time dependent advection diffusion equations for which the optimization variables are related to spatially localized quantities. Our approach uses domain decomposition applied to the optimality system to isolate the subsystem that explicitly depends on the optimization var...

Fast nonlinear programming methods following the all-at-once approach usually employ Newton’s method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton’s meth...