Related papers: ATEQ: Adaptive Toroidal Equilibrium code
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in…
A linear gyrokinetic eigenvalue code is developed to study the stability of toroidal Alfv\'en eigenmode (TAE) in general axisymmetric toroidal geometry, with the self-consistent treatment of energetic particle drive and core plasma Landau…
Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…
Adaptive gradient methods like Adagrad and its variants are widespread in large-scale optimization. However, their use of diagonal preconditioning matrices limits the ability to capture parameter correlations. Full-matrix adaptive methods,…
This work proposes for the first time a novel optimization method for numerical algorithms, which takes advantages of machine learning frameworks PyTorch and TensorRT, leveraging their modularity, low development threshold, and automatic…
It is challenging to construct metrology schemes which harness quantum features such as entanglement and coherence to surpass the standard quantum limit. We propose an ansatz for devising adaptive-feedback quantum metrology (AFQM) strategy…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of the grid relies on indicators derived from a local estimation…
The features of the TRIMEG-GKX code are described with emphasis on the exploration using novel/different schemes compared to other gyrokinetic codes, particularly the use of object-oriented programming, filter/buffer-free treatment, and a…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance…
The advancement of generalized deepfake disruption is constrained by the interruption imbalance, a fundamental bottleneck inherent to the generation of universal perturbations. We reveal that conventional static gradient normalization…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…
This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic monochrome image processing. The energy functional is based on…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data.…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…