Research Topics

My research lies at the intersection of optimization, machine learning, and scientific computing. I am interested in designing theoretically grounded and computationally efficient algorithms for large-scale problems arising in data science, networked systems, and scientific modeling. Below are several major directions of my current and past work.

Distributed Optimization Algorithms

Distributed optimization aims to solve large-scale problems collaboratively across multiple computing agents or data centers, with or without central coordination. My research explores both centralized and decentralized settings, emphasizing communication-efficient and computation-efficient algorithm design. I have developed several accelerated and provably convergent methods for decentralized gradient tracking, compressed communication, and directed network topologies—bridging theory and implementation in large-scale learning and signal processing systems.

Primal–Dual Algorithms

Primal–dual splitting methods are fundamental tools for structured convex and nonconvex optimization. I proposed the PD3O algorithm (Primal–Dual Three-Operator Splitting), which unifies and generalizes a family of primal–dual methods. My work further explores the equivalence relationships among various primal–dual frameworks, providing both mathematical insights and practical algorithms for imaging, inverse problems, and distributed learning.

Sparse Optimization and Signal Processing

Sparse modeling provides a powerful framework for recovering signals and images from limited or corrupted data. My earlier research contributed advances in nonconvex regularization, robust PCA, and low-rank matrix recovery. These works combine optimization theory with practical algorithms for image reconstruction, denoising, and compressive sensing, leading to efficient solvers with provable recovery guarantees.

Physics-Informed Neural Networks (PINNs)

Physics-Informed Neural Networks (PINNs) integrate deep learning with physical laws to solve differential equations efficiently. My recent work improves accuracy and training efficiency through novel network architectures and smoothness-regularized formulations. This research bridges traditional numerical analysis and modern AI, enabling data-driven discovery and simulation of complex physical systems.

Artificial Intelligence for Mathematical and Optimization Problems

Artificial intelligence provides new perspectives for tackling mathematical and operations research challenges. I am broadly interested in leveraging machine learning—including deep networks and reinforcement learning—to design adaptive, data-driven optimization algorithms and efficient solvers for inverse problems.

Last updated: October 2025