Related papers: Optimization methods for achieving high diffractio…
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…
A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering…
We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam splitting unitary at coarse-grained lattice sites. By demanding translational…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
We present a methodology for designing metagratings for perfect anomalous refraction, based on multilayered loaded wire arrays. In recent work, it has been shown that such structures can implement perfect anomalous deflection and beam…
Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
We propose first order algorithms for convex optimization problems where the feasible set is described by a large number of convex inequalities that is to be explored by subgradient projections. The first algorithm is an adaptation of a…
This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with…
Measurement and analysis of diffraction parameters of thick transmission holographic phase gratings recorded on PHC-488 photopolymer are presented. Precision determination of the spatial grating period is executed by Bragg angle measurement…
We use a simple effective model, obtained through the application of high-frequency homogenisation, to tackle the fundamental question of how the choice of gradient function affects the performance of a graded metamaterial. This approach…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
Graph drawing is a fundamental task in information visualization, with the Fruchterman--Reingold (FR) force model being one of the most popular choices. We can interpret this visualization task as a continuous optimization problem, which…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
Crystal structure optimization is fundamental to materials modeling but remains computationally expensive when performed with density-functional theory (DFT). Machine-learning (ML) approaches offer substantial acceleration, yet existing…
Fourier-based modal methods are among the most effective numerical tools for the accurate analysis of crossed gratings. However, leading to computationally expensive eigenvalue equations significantly restricts their applicability,…
Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a…
We propose a second-order method for unconditional minimization of functions $f(z)$ of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger derivative $\frac{\partial^2f}{\partial\bar z\partial z}$ for…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…