Jiyong Li

Jiyong Li, Dilshod Azizov, Yang Li et al.

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.

Mengting Hu, Jiyong Li, Bin Wang

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.

Bin Wang, Jiyong Li, Yonglei Fang

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.