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$\gamma$-deepDSM for interface reconstruction: operator learning and a Learning-Automated FEM package

Publication: Journal Article

Zheng, Yangyang, Huayi Wei, Shuhao Cao, and Ruchi Guo. 2024. “$\gamma$-DeepDSM for Interface Reconstruction: Operator Learning and a Learning-Automated FEM Package”. ArXiv Preprint ArXiv:2411.05341.

Robust a posteriori error estimation for finite element approximation to H(curl) problem

Publication: Journal Article

Cai, Zhiqiang, Shuhao Cao, and Rob Falgout. 2016. “Robust a Posteriori Error Estimation for Finite Element Approximation to H(curl) Problem”. Computer Methods in Applied Mechanics and Engineering 309 (1): 182-201.

Teaching

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Transformer Meets Boundary Value Inverse Problems

Publication: Conference Proceedings

Guo, Ruchi, Shuhao Cao, and Long Chen. 2023. “Transformer Meets Boundary Value Inverse Problems”. The Eleventh International Conference on Learning Representations (ICLR).

A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian

Publication: Journal Article

Barker, Mary, Shuhao Cao, and Ari Stern. 2024. “A Nonconforming Primal Hybrid Finite Element Method for the Two-Dimensional Vector Laplacian”. The SMAI Journal of Computational Mathematics 10: 85-106.

Immersed virtual element methods for electromagnetic interface problems in three dimensions

Publication: Journal Article

Cao, Shuhao, Long Chen, and Ruchi Guo. 2023. “Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions”. Mathematical Models and Methods in Applied Sciences 33 (03): 455-503.

Convergence and optimality of an adaptive modified weak Galerkin finite element method

Publication: Journal Article

Xie, Yingying, Shuhao Cao, Long Chen, and Liuqiang Zhong. 2023. “Convergence and Optimality of an Adaptive Modified Weak Galerkin Finite Element Method”. Numerical Methods for Partial Differential Equations 39 (5): 3847-73.

A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions

Publication: Journal Article

Cao, Shuhao, Chunmei Wang, and Junping Wang. 2022. “A New Numerical Method for Div-Curl Systems With Low Regularity Assumptions”. Computers & Mathematics With Applications 114: 47-59.

A recovery-based a posteriori error estimator for H(curl) interface problems

Publication: Journal Article

Cai, Zhiqiang, and Shuhao Cao. 2015. “A Recovery-Based a Posteriori Error Estimator for H(curl) Interface Problems”. Computer Methods in Applied Mechanics and Engineering 296: 169-95.

CS 5590/MATH 5555 Optimization in Machine Learning

Class

Analysis of various optimization methods and their application in training common machine learning models. Gradient descent, line search, Newton’s method, and their implementation in standard PyTorch optim interface. Specific topics include: quasi-Newton method, (stochastic) gradient descent, and momentum. Coding these methods using the optimizer class interface in PyTorch, and competing on Kaggle with your classmates.