Related papers: Solving PDE-constrained Control Problems Using Ope…

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

We address the issue of safe optimal path planning under parametric uncertainties using a novel regularizer that allows trading off optimality with safety. The proposed regularizer leverages the notion that collisions may be modeled as…

We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear)…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…

This paper investigates optimal control problems formulated over a class of piecewise-smooth vector fields. Instead of optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of…

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations…

This paper investigates solution stability properties of unregularized tracking-type optimal control problems constrained by the Boussinesq system. In our model, the controls may appear linearly and distributed in both of the equations that…

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…

The take-home message of this paper is that solving optimal control problems can be computationally straightforward, provided that differentiable partial differential equation (PDE) solvers are available. Although this might seem to be a…

We consider a PDE-constrained optimization problem governed by a free boundary problem. The state system is based on coupling the Laplace equation in the bulk with a Young-Laplace equation on the free boundary to account for surface…

We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…

This article builds on the recently proposed RB-ML-ROM approach for parameterized parabolic PDEs and proposes a novel hierarchical Trust Region algorithm for solving parabolic PDE constrained optimization problems. Instead of using a…

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…