相关论文: On some Operator Filtering Strategies Based on Sui…

We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.…

A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n…

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…

This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…

The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…

Model Order Reduction is a key technology for industrial applications in the context of digital twins. Key requirements are non-intrusiveness, physics-awareness, as well as robustness and usability. Operator inference based on least-squares…

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This paper proposes…

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic…

Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

The combination of energy harvesting and large-scale multiple antenna technologies provides a promising solution for improving the energy efficiency (EE) by exploiting renewable energy sources and reducing the transmission power per user…

Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation…

Optimisation problems, particularly combinatorial optimisation problems, are difficult to solve due to their complexity and hardness. Such problems have been successfully solved by evolutionary and swarm intelligence algorithms, especially…

Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.

We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…

Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…