Yuze Hao

Zhentao Tan, Yuze Hao, Boyi Zou et al.

Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging, geophysics, materials science, and aerodynamics, where the goal is to infer hidden causes, design structures, or control physical states. In this paper, we provide a comprehensive review of recent advances in solving inverse PDE problems using artificial intelligence (AI). We first introduce the basic formulation, key challenges, and traditional numerical foundations of inverse PDE problems, and then organize it into three major categories: inverse problems, inverse design, and control problems. For each category, we further present a methodological paradigms, and review representative state-of-the-art approaches from recent years. We then summarize representative applications across scientific and industrial domains, including mechanical systems, aerodynamic problems, thermal systems, full-waveform inversion, system identification, and medical imaging. Finally, we discuss open challenges and future prospects, such as physics-informed architectures, limited real-world data, uncertainty quantification, and inverse foundation models. This survey aims to provide the first unified and systematic perspective on AI for inverse PDE problems, demonstrating how modern learning-based methods are reshaping inverse problems, inverse design, and control problems in PDE-governed systems.

Yuze Hao, Jianrong Zhang, Tao Zhuo et al.

Hands are the main medium when people interact with the world. Generating proper 3D motion for hand-object interaction is vital for applications such as virtual reality and robotics. Although grasp tracking or object manipulation synthesis can produce coarse hand motion, this kind of motion is inevitably noisy and full of jitter. To address this problem, we propose a data-driven method for coarse motion refinement. First, we design a hand-centric representation to describe the dynamic spatial-temporal relation between hands and objects. Compared to the object-centric representation, our hand-centric representation is straightforward and does not require an ambiguous projection process that converts object-based prediction into hand motion. Second, to capture the dynamic clues of hand-object interaction, we propose a new architecture that models the spatial and temporal structure in a hierarchical manner. Extensive experiments demonstrate that our method outperforms previous methods by a noticeable margin.