arXiv subjects

Jiyong Li

Publications and source records attributed to Jiyong Li.

4 recordsLinked to original sources

arXiv2026

Improved error estimates of a new splitting scheme for charged-particle dynamics in strong magnetic field with maximal ordering

This paper introduces a novel second-order splitting scheme for charged-particle dynamics in strong magnetic fields characterized by the maximal ordering. The proposed scheme is explicit and symmetric, which respectively ensure the efficiency of the algorithm and its long-term near-conservation of energy. We rigorously prove that the scheme achieves improved error bounds for both the position and the velocity component parallel to the magnetic field, yielding a uniform second-order error bound under specific strong-field regimes. Numerical experiments confirm the optimal convergence rates and the long-term energy near conservation of the method.

math.NA↗

arXiv2025

Fourth-order uniformly accurate integrators with long time near conservations for the nonlinear Dirac equation in the nonrelativistic regime

In this paper, we propose two novel fourth-order integrators that exhibit uniformly high accuracy and long-term near conservations for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime. In this regime, the solution of the NLDE exhibits highly oscillatory behavior in time, characterized by a wavelength of O($\varepsilon^{2}$) with a small parameter $\varepsilon>0$. To ensure uniform temporal accuracy, we employ a two-scale approach in conjunction with exponential integrators, utilizing operator decomposition techniques for the NLDE. The proposed methods are rigorously proved to achieve fourth-order uniform accuracy in time for all $\varepsilon\in (0,1]$. Furthermore, we successfully incorporate symmetry into the integrator, and the long-term near conservation properties are analyzed through the modulated Fourier expansion. The proposed schemes are readily extendable to linear Dirac equations incorporating magnetic potentials, the dynamics of traveling wave solutions and the two/three-dimensional Dirac equations. The validity of all theoretical ndings and extensions is numerically substantiated through a series of numerical experiments.

math.NA↗

arXiv2024

Contrastive Continual Learning with Importance Sampling and Prototype-Instance Relation Distillation

Recently, because of the high-quality representations of contrastive learning methods, rehearsal-based contrastive continual learning has been proposed to explore how to continually learn transferable representation embeddings to avoid the catastrophic forgetting issue in traditional continual settings. Based on this framework, we propose Contrastive Continual Learning via Importance Sampling (CCLIS) to preserve knowledge by recovering previous data distributions with a new strategy for Replay Buffer Selection (RBS), which minimize estimated variance to save hard negative samples for representation learning with high quality. Furthermore, we present the Prototype-instance Relation Distillation (PRD) loss, a technique designed to maintain the relationship between prototypes and sample representations using a self-distillation process. Experiments on standard continual learning benchmarks reveal that our method notably outperforms existing baselines in terms of knowledge preservation and thereby effectively counteracts catastrophic forgetting in online contexts. The code is available at https://github.com/lijy373/CCLIS.

cs.LG↗

arXiv2018

Long-term analysis of exponential integrators for highly oscillatory conservative systems

In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.

math.NA↗