Distributed Algorithms

We design centralized and decentralized methods for large-scale learning over networks, with an emphasis on communication-efficient and computation-efficient algorithms. Topics include gradient tracking, compressed communication, directed network topologies, and federated or decentralized training.

Slides: Decentralized Consensus Algorithms

Physics-Informed Neural Networks

We develop optimization perspectives, model architectures, and regularization tools for physics-informed neural networks. The goal is to make neural methods more accurate, stable, and efficient for differential equations and scientific simulation.

Primal-Dual Algorithms

We study splitting methods for structured convex and nonconvex optimization, including PD3O and related primal-dual frameworks. These methods are useful in imaging, inverse problems, signal processing, and distributed learning.

Slides: Primal-Dual Algorithms

Sparse Optimization and Signal Processing

We work on sparse modeling, nonconvex regularization, robust PCA, low-rank recovery, image reconstruction, denoising, and compressive sensing. These problems connect optimization theory with concrete computational tools.

AI for Mathematical and Optimization Problems

We are interested in using machine learning, deep networks, and reinforcement learning to design adaptive algorithms and efficient solvers for mathematical, optimization, and inverse problems.

分布式优化算法

我们研究面向大规模网络学习的集中式与去中心化优化方法，重点关注通信高效和计算高效的算法设计。相关主题包括梯度跟踪、压缩通信、有向网络拓扑，以及联邦或去中心化训练。

讲义：去中心化一致性算法

物理信息神经网络

我们从优化角度研究物理信息神经网络，发展新的模型结构和正则化工具，希望提升其在微分方程和科学模拟中的精度、稳定性与训练效率。

原始-对偶算法

我们研究结构化凸与非凸优化中的分裂方法，包括 PD3O 算法以及相关原始-对偶框架。这类方法可应用于成像、反问题、信号处理和分布式学习。

讲义：原始-对偶算法

稀疏优化与信号处理

我们研究稀疏建模、非凸正则化、鲁棒 PCA、低秩恢复、图像重建、去噪和压缩感知等问题。这些方向将优化理论与实际计算工具紧密联系起来。

面向数学与优化问题的人工智能

我们关注如何利用机器学习、深度网络和强化学习来设计自适应算法，并为数学、优化和反问题构建高效求解器。