Yichi Zhang

Zhongkai Hao, Songming Liu, Yichi Zhang et al. · tsinghua

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from being fully explored in the field of physics-informed machine learning. We believe that the interdisciplinary research of physics-informed machine learning will significantly propel research progress, foster the creation of more effective machine learning models, and also offer invaluable assistance in addressing long-standing problems in related disciplines.

Zhongkai Hao, Jiachen Yao, Chang Su et al.

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

Yichi Zhang, Gongwei Chen, Jun Zhu et al.

Visual grounding requires large and diverse region-text pairs. However, manual annotation is costly and fixed vocabularies restrict scalability and generalization. Existing pseudo-labeling pipelines often overfit to biased distributions and generate noisy or redundant samples. Through our systematic analysis of data quality and distributional coverage, we find that performance gains come less from raw data volume and more from effective distribution expansion. Motivated by this insight, we propose DAL, a distribution-aware labeling framework for visual grounding. The proposed method first employs a dual-driven annotation module, where a closed-set path provides reliable pseudo labels and an open-set path enriches vocabulary and introduces novel concepts; meanwhile, it further performs explicit out-of-distribution (OOD) expression expansion to broaden semantic coverage. We then propose a consistency- and distribution-aware filtering module to discard noisy or redundant region-text pairs and rebalance underrepresented linguistic and visual content, thereby improving both data quality and training efficiency. Extensive experiments on three benchmarks demonstrate that our method consistently outperforms strong baselines and achieves state-of-the-art results, underscoring the critical role of distribution-aware labeling in building scalable and robust visual grounding datasets.

Yichi Zhang, Minh Tang

Random-walk based network embedding algorithms like DeepWalk and node2vec are widely used to obtain Euclidean representation of the nodes in a network prior to performing downstream inference tasks. However, despite their impressive empirical performance, there is a lack of theoretical results explaining their large-sample behavior. In this paper, we study node2vec and DeepWalk through the perspective of matrix factorization. In particular, we analyze these algorithms in the setting of community detection for stochastic blockmodel graphs (and their degree-corrected variants). By exploiting the row-wise uniform perturbation bound for leading singular vectors, we derive high-probability error bounds between the matrix factorization-based node2vec/DeepWalk embeddings and their true counterparts, uniformly over all node embeddings. Based on strong concentration results, we further show the perfect membership recovery by node2vec/DeepWalk, followed by $K$-means/medians algorithms. Specifically, as the network becomes sparser, our results guarantee that with large enough window size and vertices number, applying $K$-means/medians on the matrix factorization-based node2vec embeddings can, with high probability, correctly recover the memberships of all vertices in a network generated from the stochastic blockmodel (or its degree-corrected variants). The theoretical justifications are mirrored in the numerical experiments and real data applications, for both the original node2vec and its matrix factorization variant.