Related papers: Forward-Mode Differentiation of Maxwell's Equation…
This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investigate three canonical classes of models: nonlinear impedance,…
Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…
We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law.…
In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method…
Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…
Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
We propose high-order FDTD schemes based on the Correction Function Method (CFM) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not…
Supervised learning in deep neural networks is commonly performed using error backpropagation. However, the sequential propagation of errors during the backward pass limits its scalability and applicability to low-powered neuromorphic…
A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed,…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…
Multispectral pedestrian detection has been shown to be effective in improving performance within complex illumination scenarios. However, prevalent double-stream networks in multispectral detection employ two separate feature extraction…