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Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…
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.…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
We propose MHR-Net, a novel method for recovering Non-Rigid Shapes from Motion (NRSfM). MHR-Net aims to find a set of reasonable reconstructions for a 2D view, and it also selects the most likely reconstruction from the set. To deal with…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
In this paper we study the problem of characterizing and computing the nonanticipative rate distortion function (NRDF) for partially observable multivariate Gauss-Markov processes with hard mean squared error (MSE) distortion constraints.…
Optimal inverse design, including topology optimization and evaluation of fundamental bounds on performance, which was introduced in Part~1, is applied to various antenna design problems. A memetic scheme for topology optimization combines…
Intelligent reflecting surface (IRS) is an emerging technology to enhance spatial multiplexing in wireless networks. This letter considers the discrete passive beamforming design for IRS in order to maximize the minimum…
This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming…
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them…
We propose a penalty-based smoothing framework for convex nonsmooth functions with a supremum structure. The regularization yields a differentiable surrogate with controlled approximation error, a single-valued dual maximizer, and explicit…
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes.…
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…