Yupeng Jiang

Zhaofeng Luo, Minchen Li, Yupeng Jiang

We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The method decomposes the domain into overlapping coarse and fine subdomains with heterogeneous spatial and temporal resolutions, while retaining standard MPM discretizations within each subdomain. Coarse-fine coupling is achieved through an MPM-specific Schwarz iteration combining mass-weighted spatial transmission and temporal interpolation for sub-cycling. In contrast to refinement strategies based on modified basis functions, transition kernels, or strongly enforced interface constraints, the proposed approach preserves the modular structure of standard MPM and shifts the coupling complexity to nonmatching-grid interface operators within the Schwarz alternating procedure. Numerical examples, including a gravity-driven cantilever beam, Hertzian contact, and an elastic inclusion problem, show that the method reproduces analytical or fine-resolution reference solutions with good accuracy and convergence behavior. In the inclusion benchmark, the proposed framework achieves comparable or slightly lower error than single-domain fine simulations at the finest tested resolutions, while reducing computational cost by up to 9.15 times. A three-dimensional folding example further demonstrates the generality of the framework. These results indicate that the proposed method provides an accurate, modular, and efficient route for local space-time refinement in MPM.

Qirui Fu, Yupeng Jiang, Minchen Li

The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although wide-support smooth kernels can effectively suppress cell-crossing instability, they often introduce increased numerical diffusion, artificial contact gaps, and higher transfer cost. In contrast, the suitability of compact-kernel designs for implicit computational solid mechanics remains unclear. In this work, we develop an implicit formulation of the Compact-Kernel Material Point Method (CK-MPM) and assess its performance through benchmark problems in linear and nonlinear solid mechanics, including cantilever bending, Hertzian contact, narrow-clearance free fall, and colliding hyperelastic rings. The results show that implicit CK-MPM retains the advantages of compact support while preserving the smoothness required for robust large-deformation simulation. Compared with linear MPM, it reduces cell-crossing-induced stress noise and excessive numerical dissipation; compared with quadratic B-spline MPM, it improves contact locality and reduces artificial contact gaps and early-contact artifacts while maintaining comparable overall smoothness and accuracy. These results indicate that CK-MPM provides a viable implicit MPM framework for computational mechanics.

Yupeng Jiang, Yong Li, Yipeng Zhou et al.

In federated learning, machine learning and deep learning models are trained globally on distributed devices. The state-of-the-art privacy-preserving technique in the context of federated learning is user-level differential privacy. However, such a mechanism is vulnerable to some specific model poisoning attacks such as Sybil attacks. A malicious adversary could create multiple fake clients or collude compromised devices in Sybil attacks to mount direct model updates manipulation. Recent works on novel defense against model poisoning attacks are difficult to detect Sybil attacks when differential privacy is utilized, as it masks clients' model updates with perturbation. In this work, we implement the first Sybil attacks on differential privacy based federated learning architectures and show their impacts on model convergence. We randomly compromise some clients by manipulating different noise levels reflected by the local privacy budget epsilon of differential privacy on the local model updates of these Sybil clients such that the global model convergence rates decrease or even leads to divergence. We apply our attacks to two recent aggregation defense mechanisms, called Krum and Trimmed Mean. Our evaluation results on the MNIST and CIFAR-10 datasets show that our attacks effectively slow down the convergence of the global models. We then propose a method to keep monitoring the average loss of all participants in each round for convergence anomaly detection and defend our Sybil attacks based on the prediction cost reported from each client. Our empirical study demonstrates that our defense approach effectively mitigates the impact of our Sybil attacks on model convergence.

Lakshmi Sirisha Revadi, Xi Zheng, Yupeng Jiang

Software as a Service (SaaS) is well established as an effective model for the development, deployment and customization of software. As it continues to gain more momentum in the IT industry, many user experience challenges and issues are being reported by the experts and end users.