Related papers: Integrated photonic multigrid solver for partial d…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image…
The Galton board is a desktop probability machine traditionally used to visualize the principles of statistical physics with classical particles. Here, we demonstrate a photonic Galton board that enables on-chip observation of single-photon…
The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…
Universal quantum computing requires an architecture that supports both linear circuits and, crucially, strong nonlinear resources. For quantum photonic systems, integrating such nonlinearities with scalable linear circuitry has been a…
Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…
Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order…
Image slicing is a powerful technique in astronomy. It allows the instrument designer to reduce the slit width of the spectrograph, increasing spectral resolving power whilst retaining throughput. Conventionally this is done using bulk…
This paper proposes to adopt advanced monolithic silicon-photonics integrated-circuits manufacturing capabilities to achieve a system-on-chip photonic-electronic linear-algebra accelerator with the features of optical comb-based broadband…
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Network Multigrid Solver (DNN-MG), (Margenberg et al., J Comput…
We present a polynomial multigrid method for nodal interior penalty and local discontinuous Galerkin formulations of the Poisson equation on Cartesian grids. For smoothing we propose two classes of overlapping Schwarz methods. The first…
Multi-focus image fusion is a challenging field of study that aims to provide a completely focused image by integrating focused and un-focused pixels. Most existing methods suffer from shift variance, misregistered images, and…
Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
Photonic integrated circuits are facilitating the development of optical neural networks, which have the potential to be both faster and more energy efficient than their electronic counterparts since optical signals are especially…