Dong Sun

Wenbin Chen, Max Gunzburger, Dong Sun et al.

We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the second-order Gear's extrapolation approach. The second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of two decoupled problems at each time step, one Stokes and the other Darcy. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. The uniform in time stability leads to uniform in time control of the error which is highly desirable for modeling physical processes, e.g., contaminant sequestration and release, that occur over very long time scales. Error estimates for fully-discretized schemes using finite element spatial discretizations are derived. Numerical examples are provided that illustrate the accuracy, efficiency, and long-time stability of the two schemes.

Dong Sun, Rahul Nittala, Rebekka Burkholz

Despite their practical success, it remains unclear why Mixture of Experts (MoE) models can outperform dense networks beyond sheer parameter scaling. We study an iso-parameter regime where inputs exhibit latent modular structure but are corrupted by feature noise, a proxy for noisy internal activations. We show that sparse expert activation acts as a noise filter: compared to a dense estimator, MoEs achieve lower generalization error under feature noise, improved robustness to perturbations, and faster convergence speed. Empirical results on synthetic data and real-world language tasks corroborate the theoretical insights, demonstrating consistent robustness and efficiency gains from sparse modular computation.

Zhuoyuan Wang, Dong Sun, Xiangyun Zeng et al.

The segmentation of organs in volumetric medical images plays an important role in computer-aided diagnosis and treatment/surgery planning. Conventional 2D convolutional neural networks (CNNs) can hardly exploit the spatial correlation of volumetric data. Current 3D CNNs have the advantage to extract more powerful volumetric representations but they usually suffer from occupying excessive memory and computation nevertheless. In this study we aim to enhance the 2D networks with contextual information for better volumetric image segmentation. Accordingly, we propose a contextual embedding learning approach to facilitate 2D CNNs capturing spatial information properly. Our approach leverages the learned embedding and the slice-wisely neighboring matching as a soft cue to guide the network. In such a way, the contextual information can be transferred slice-by-slice thus boosting the volumetric representation of the network. Experiments on challenging prostate MRI dataset (PROMISE12) and abdominal CT dataset (CHAOS) show that our contextual embedding learning can effectively leverage the inter-slice context and improve segmentation performance. The proposed approach is a plug-and-play, and memory-efficient solution to enhance the 2D networks for volumetric segmentation. Our code is publicly available at https://github.com/JuliusWang-7/CE_Block.