相关论文: Shape optimization for superconductors governed by…
In this paper, we design a controller for an interconnected system composed of a linear Stochastic Differential Equation (SDE) controlled through a linear hetero-directional hyperbolic Partial Differential Equation (PDE). Our objective is…
In this work, we discuss the task of finding a direction of optimal descent for problems in Shape Optimisation and its relation to the dual problem in Optimal Transport. This link was first observed in a previous work which sought…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…
In this paper, we present a convex formulation of $H_{\infty}$-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE)…
In this paper, we study an optimal exit time problem with general running and terminal costs and a target $\mathcal{S}\subset\mathbb{R}^d$ having an inner ball property for a nonlinear control system that satisfies mild controllability…
One fundamental problem in decentralized multi-agent optimization is the trade-off between gradient/sampling complexity and communication complexity. We propose new algorithms whose gradient and sampling complexities are graph topology…
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to…
This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…
This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape under investigation, as well as on intrinsic shape metrics.…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
In the presented study, a pipe penalization approach for the economic topology optimization of District Heating Networks is proposed, drawing inspiration from density-based topology optimization. For District Heating Networks, the upfront…
In this paper we consider the free-form optimization of eigenvalues in electromagnetic systems by means of shape-variations with respect to small deformations. The objective is to optimize a particular eigenvalue to a target value. We…