Jaemin Shin

Jaemin Shin, Hyun Geun Lee, June-Yub Lee

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

Adiba Orzikulova, Jaehyun Kwak, Jaemin Shin et al.

Many healthcare sensing applications utilize multimodal time-series data from sensors embedded in mobile and wearable devices. Federated Learning (FL), with its privacy-preserving advantages, is particularly well-suited for health applications. However, most multimodal FL methods assume the availability of complete modality data for local training, which is often unrealistic. Moreover, recent approaches tackling incomplete modalities scale poorly and become inefficient as the number of modalities increases. To address these limitations, we propose FLISM, an efficient FL training algorithm with incomplete sensing modalities while maintaining high accuracy. FLISM employs three key techniques: (1) modality-invariant representation learning to extract effective features from clients with a diverse set of modalities, (2) modality quality-aware aggregation to prioritize contributions from clients with higher-quality modality data, and (3) global-aligned knowledge distillation to reduce local update shifts caused by modality differences. Extensive experiments on real-world datasets show that FLISM not only achieves high accuracy but is also faster and more efficient compared with state-of-the-art methods handling incomplete modality problems in FL. We release the code as open-source at https://github.com/AdibaOrz/FLISM.