Related papers: Optimal Boundary Discretization by Variational Dat…
In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the…
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…
Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…
In this work, we use the integral definition of the fractional Laplace operator and study a sparse optimal control problem involving a fractional, semilinear, and elliptic partial differential equation as state equation; control constraints…
This paper is concerned with eigenvalue problems for non-symmetric elliptic operators with large drifts in bounded domains under Dirichlet boundary conditions. We consider the minimal principal eigenvalue and the related principal…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Learning algorithms that learn linear models often have high representation bias on real-world problems. In this paper, we show that this representation bias can be greatly reduced by discretization. Discretization is a common procedure in…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Nonlinear aggregation is central to modern distributed systems, yet its privacy behavior is far less understood than that of linear aggregation. Unlike linear aggregation where mature mechanisms can often suppress information leakage,…
We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the…
Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. The weights given to the observations and background state depend on their specified error…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…