Zhen Liao

Shuwei Zhou, Christian Haeffner, Shuancheng Wang et al.

Physics-informed neural networks have been widely applied to solid mechanics problems. However, balancing the governing partial differential equations and boundary conditions remains challenging, particularly in fracture mechanics, where accurate predictions strongly depend on refined sampling near crack tips. To overcome these limitations, a Kolosov-Muskhelishvili informed neural network with Williams enrichment is developed in this study. Benefiting from the holomorphic representation, the governing equations are satisfied by construction, and only boundary points are required for training. Across a series of benchmark problems, the Kolosov-Muskhelishvili informed neural network shows excellent agreement with analytical and finite element method references, achieving average relative errors below 1\% and $R^2$ above 0.99 for both mode I and mode II loadings. Furthermore, three crack propagation criteria (maximum tangential stress, maximum energy release rate, and principle of local symmetry) are integrated into the framework using a transfer learning strategy to predict crack propagation directions. The predicted paths are nearly identical across all criteria, and the transfer learning strategy reduces the required training time by more than 70\%. Overall, the developed framework provides a unified, mesh-free, and physically consistent approach for accurate and efficient crack propagation analysis.

Zhen Liao

While numerous studies have been conducted in the literature exploring different types of machine learning approaches for search ranking, most of them are focused on specific pre-defined problems but only a few of them have studied the ranking framework which can be applied in a commercial search engine in a scalable way. In the meantime, existing ranking models are often optimized for normalized discounted cumulative gains (NDCG) or online click-through rate (CTR), and both types of machine learning models are built based on the assumption that high-quality training data can be easily obtained and well applied to unseen cases. In practice at Facebook search, we observed that our training data for ML models have certain issues. First, tail query intents are hardly covered in our human rating dataset. Second, search click logs are often noisy and hard to clean up due to various reasons. To address the above issues, in this paper, we propose a probabilistic intent based ranking framework (short for piRank), which can: 1) provide a scalable framework to address various ranking issues for different query intents in a divide-and-conquer way; 2) improve system development agility including iteration speed and system debuggability; 3) combine both machine learning and empirical-based algorithmic methods in a systematic way. We conducted extensive experiments and studies on top of Facebook search engine system and validated the effectiveness of this new ranking architecture.