arXiv subjects

Jiale Gao

Publications and source records attributed to Jiale Gao.

6 recordsLinked to original sources

arXiv2025

A Surrogate model for High Temperature Superconducting Magnets to Predict Current Distribution with Neural Network

Finite element methods (FEM) for high-temperature superconducting (HTS) magnets become time-consuming at larger scales, restricting the rapid optimization of meter-scale REBCO solenoids. In this work, a surrogate model based on a fully connected residual neural network (FCRN) is developed to predict the current density distribution in REBCO solenoids. Trained on datasets generated from FEM simulations by the T-A formulation, the FCRN model is evaluated under both fast ramping and steady-state scenarios, showing a lower validation loss than the fully connected network (FCN). When extrapolating geometric parameters beyond the training set, the model achieves a relative error of below 10 % for magnetization losses in Case 1 and an average error of 1.2 % for the central magnetic field in Case 2. Furthermore, deploying the steady-state surrogate model for rapid magnet design found the optimal solution within the parameter space under constraints, with a relative central magnetic field error of 0.2 % compared to FEM results. With rapid predictions, this surrogate model offers an efficient tool for the intelligent design of large-scale HTS magnets.

cs.LG↗

arXiv2024

The W-weighted m-weak group MP inverse and its applications

We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties, characterizations and representations of this new generalized inverse are shown. Additionally, applications of the W-weighted weak group MP inverse are given in solving a constrained optimization problem and a class of consistent matrix equations.

math.FA↗

arXiv2024

m-weak group MP inverse

In this paper, we introduce a new matrix decomposition called the m-Core-nilpotent decomposition which is an extension of the Core-nilpotent decomposition. By this new decomposition, we propose a new generalized inverse named the m-weak group MP inverse which unifies the DMP-inverse and weak core inverse. Some characterizations, properties and representations of the m-weak group MP inverse are presented. In addition, the proposed generalized inverse is applicable to solving a restricted matrix equation.

math.RA↗

arXiv2023

Further properties and representations of the W-weighted m-weak group inverse

The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted weak group inverse, W-weighted core inverse, etc. We also give three concise explicit expressions for the W-m-WG inverse. Moreover, a canonical form of the W-m-WG inverse is presented in terms of the singular value decomposition. Finally, several numerical examples are designed to illustrate some results given in the paper.

math.RA↗

arXiv2023

The m-DMP inverse in Minkowski space and its applications

This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges, null spaces and matrix equations, and show its integral and limiting representations and several explicit expressions. Finally, the paper gives applications of the m-DMP inverse in solving a system of linear equations and a constrained optimization problem.

math.OC↗

arXiv2023

Further characterizations and representations of the Minkowski inverse in Minkowski space

This paper is aimed to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of {1,3m}, {1,2,3m}, {1,4m} and {1,2,4m}-inverses are given in order to represent the Minkowski inverse. Secondly, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Thirdly, using the Hartwig-Spindelböck decomposition we present a representation of the Minkowski inverse. And, based on this result, an interesting characterization of the Minkowski inverse is showed by a rank equation. Finally, we obtain several new representations of the Minkowski inverse in a more general form, by which the Minkowski inverse of a class of block matrices is given.

math.FA↗