Related papers: Computational Bounds For Photonic Design
Probabilistic computing excels in approximating combinatorial problems and modelling uncertainty. However, using conventional deterministic hardware for probabilistic models is challenging: (pseudo) random number generation introduces…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
The physical implementation of artificial intelligence requires mapping computational processes onto the dynamic physical processes of the underlying computing platform. The photonic processors offer an intrinsically parallel and low energy…
Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…
This article deals with optimizing problems classified by the kinds of restrictions as required in differential geometry and in mechanics: holonomic and nonholonomic. The central issue relates to dual nonholonomic programs (what they mean…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
A computationally-fast inverse design method for nanophotonic structures is presented. The method is based on two complementary convex optimization problems which modify the dielectric structure and resonant field respectively. The design…
In contrast to designing nanophotonic devices by tuning a handful of device parameters, we have developed a computational method which utilizes the full parameter space to design linear nanophotonic devices. We show that our method may…
Atomic transitions with orthogonal dipole moments can be made to interfere with each other by the use of an anisotropic environment. Here we describe, provide and apply a computational toolbox capable of algorithmically designing…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
Recently, there has been considerable interest in solving optimization problems by mapping these onto a binary representation, sparked mostly by the use of quantum annealing machines. Such binary representation is reminiscent of a discrete…
We introduce a new method for inverse design of nanophotonic devices which guarantees that resulting designs satisfy strict length scale constraints - including minimum width and spacing constraints required by commercial semiconductor…
Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Under a geometric assumption on the region near the end of its neck, we prove an optimal exponential lower bound on the widths of resonances for a general two-dimensional Helmholtz resonator. An extension of the result to the n-dimensional…