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Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Category-level object pose estimation aims to predict the pose and size of arbitrary objects in specific categories. Existing methods struggle with the inherent incompleteness of observed point clouds, which limits their ability to capture…
In this paper a new method for spotsize-measurement for singlemode optical components is presented. Based from the classical farfield-method where the measurements are made circular, the mounting of the used rotary stages and the long…
We present an open geometry Fourier modal method based on a new combination of open boundary conditions and an efficient $k$-space discretization. The open boundary of the computational domain is obtained using basis functions that expand…
A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric…
We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and…
Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…
Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…
In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…
Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…
This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with…
Some metrological means, such as Shack-Hartmann, deflectometry sensors or fringe projection profilometry, measure the shape of an optical surface indirectly from slope measurements. Zonal shape reconstruction, a method to reconstruct shape…
The problem of scattering of linear internal waves from small compact sea bottom inhomogeneities is considered from the point of view of mode-to-mode scattering. A simple formula for modal conversion coefficients, quantifying the amount of…
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for…
Characteristic Mode analysis is a widely used technique in antenna design, providing insight into the fundamental electromagnetic properties of radiating structures. In this paper, we establish fundamental bounds on the slope of…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
We develop a non invasive method for determine morphometric caracteristic of individuals. We modelize a individual by a polyarticulated chain of rigid segments and each of these segments corresponds to a volume. For this, each segment is…
This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient…
A method to infer and synthetically extrapolate roughness fields from electron microscope scans of additively manufactured surfaces using an adaptation of Rogallo's synthetic turbulence method [R. S. Rogallo, NASA Technical Memorandum…