Yue Yu

Yue Yu is a Professor in the Department of Mathematics at Lehigh University, specializing in applied mathematics and computational mathematics. Their research focuses on hybrid modeling, physics-informed machine learning, and nonlocal operators for material science and engineering applications. Yu has developed innovative methods for data-driven constitutive law discovery, peridynamic modeling, and causal graph learning. Their work bridges computational mathematics with real-world challenges in materials, biomedical systems, and fluid-structure interactions.

Key research directions include operator learning frameworks (e.g., neural operators, nonlocal attention mechanisms), physics-guided smoothing techniques for material modeling, and scalable causal inference algorithms. Yu has pioneered methods like the Peridynamic Neural Operator (PNO) and Embedded Nonlocal Operator Regression (ENOR), advancing nonlocal calculus applications. Their contributions span interdisciplinary areas such as metamaterial design, fracture mechanics, and biomedical tissue modeling using digital image correlation.

Publications emphasize methodological advancements in operator networks, DAG learning, and asymptotically compatible numerical methods. Yu has explored meta-learning for physics discovery and developed frameworks for integrating finite elements with deep neural operators. Current work addresses high-dimensional systems, data-scarce scenarios, and uncertainty quantification in complex material systems.

Lab activities focus on computational modeling, numerical analysis, and AI-driven scientific computing. Collaborations involve engineering, physics, and biomedical domains. Yu's research is supported by leading journals in computational mathematics and has been recognized in conferences like the ASME Summer Bioengineering Conference.