Computation & Intelligence 

Research Overview:

Prof. Yang develops mathematical foundations and computational methods for intelligent scientific computing. His research lies at the intersection of applied mathematics, scientific computing, machine learning, and artificial intelligence, with the goal of building principled algorithms that can model, simulate, optimize, and discover complex scientific systems.

His work combines mathematical structure with data-driven intelligence. Earlier research focused on applied harmonic analysis, randomized numerical linear algebra, fast algorithms, and high-dimensional computation. His current research advances AI for scientific computing, including deep learning theory, machine-learning-based solvers for PDEs and inverse problems, scientific foundation models, reduced-order modeling, symbolic and interpretable learning, reinforcement learning for intelligent computation, quantum algorithms, and agentic AI systems for computational science and engineering.

Current research directions include:

• AutoNumerics: Agentic AI for Computational Science and Engineering [statement] 

This project develops agentic AI frameworks for automating and augmenting scientific computing. The goal is to design AI systems that can formulate computational problems, search over numerical strategies, generate and test implementations, verify results, and refine scientific workflows. A central theme is to combine large language models, symbolic representations, structured search, numerical analysis, and verification mechanisms to create trustworthy AI systems for computational science and engineering.

• Symbolic and Interpretable Machine Learning [statement]

This research develops machine learning methods that discover symbolic, analytical, or mechanistic structure from data. It includes symbolic regression, finite-expression methods, interpretable reinforcement learning, and AI-guided discovery of governing equations, computational models, and reduced representations. The long-term goal is to move beyond black-box prediction toward machine learning systems that produce human-understandable scientific knowledge.

• Mathematical Foundations of Deep Learning [statement]

This direction studies the theoretical principles underlying deep neural networks and modern representation learning. Topics include approximation theory, optimization dynamics, implicit regularization, expressivity, generalization, and the geometry of neural network training. The goal is to understand both what deep networks can represent and what training algorithms can reliably discover, especially in high-dimensional scientific and data-driven problems.

• Machine Learning for PDEs, Inverse Problems, and Dynamical Systems [statement]

This research develops and analyzes machine learning methods for solving partial differential equations, high-dimensional dynamical systems, and inverse problems. It includes neural-network-based PDE solvers, operator learning, physics-informed learning, mesh-free methods, and hybrid approaches that integrate numerical analysis with modern machine learning. The emphasis is on accuracy, scalability, stability, and mathematical reliability.

• Scientific Foundation Models, Reduced Modeling, and Prediction [statement]

This direction develops data-driven and structure-preserving methods for learning efficient representations of complex dynamical systems. Topics include reduced-order modeling, system identification, time-series prediction, uncertainty-aware forecasting, and scientific foundation models for simulation and prediction. The goal is to build models that are not only computationally efficient, but also transferable, interpretable, and faithful to the underlying scientific structure.

• Randomized Algorithms, Optimization, and Scientific Data Science

This line of work develops fast randomized algorithms for large-scale computation, numerical linear algebra, data analysis, and imaging. Topics include randomized sampling, sketching, matrix approximation, dimension reduction, and efficient algorithms for high-dimensional scientific data. The emphasis is on methods that are theoretically grounded, scalable, and effective in modern computational environments.

• Quantum Algorithms and Scientific Computing

Overall, Prof. Yang’s research seeks to establish a rigorous foundation for the next generation of scientific computing: computational systems that are data-adaptive but mathematically grounded, automated but verifiable, expressive but interpretable, and capable of accelerating discovery across science and engineering.

Publications:

• For a full list of publications, see Google Shcolar [link]

Agentic AI and Applications to Computationa & Science [statement]

Reinforcement Learning (RL):

Deep Learning:

Quantum Computing:

Scientific Computing:

Signal, Image, and Data Science:

Prof. Yang’s research has been supported by the National Science Foundation, the Office of Naval Research, DARPA, the Department of Energy, Oracle, NVIDIA, and the University of Maryland.