Overview
My research encompasses (1) the development of efficient algorithms that address fundamental computational issues in applications like molecular dynamics, quantum chemistry, inverse problems, machine learning and deep learning, etc.
(2) the mathematical analysis that reveals the "lubricant" and caveats when dealing with computationally challenging problems ranging from low to high dimensions.
Research Interests
- Neural Networks, Generative Models, Variational Inference
- Low-rank Approximations, Hierarchical Matrices, N-body Simulations
- Adaptive Schemes, Fast Algorithms, Quantum Chemistry
- Topics named after Bayes, Fourier, Gauss, Monte Carlo, Newton, ... ...
Publications
- [ link ][ view ]
D. Cai, E. Chow, L. Erlandson, Y. Saad, and Y. Xi,
SMASH: Structured Matrix Approximation by Separation and Hierarchy
Numerical Linear Algebra with Applications (2018)
- [ link ][ view ]
D. Cai, Z. Cai,
A Hybrid A Posteriori Error Estimator for Conforming Finite Element Approximations
Comput. Methods Appl. Mech. Eng., 339 (2018), 320-340
- [ link ][ view ]
D. Cai and P. S. Vassilevski,
Eigenvalue Problems for Exponential Type Kernels
Computational Methods in Applied Mathematics, 20(1), pp. 61-78. (2019)
- [ link ][ view ]
D. Cai, Z. Cai, and S. Zhang,
Robust Equilibrated A Posteriori Error Estimator for Higher Order Finite Element Approximations to Diffusion Problems
Numerische Mathematik, 144, pp. 1-21(2020)
- [ link ][ view ]
L. Erlandson, D. Cai, Y. Xi, and E. Chow,
Accelerating Parallel Hierarchical Matrix-Vector Products via Data-Driven Sampling
34th IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 749-758 (2020)
- [ link ][ view ]
D. Cai, J. Xia,
A Stable Matrix Version of The Fast Multipole Method: Stabilization Strategies and Examples
Electronic Transactions on Numerical Analysis, accepted
- [ link ][ view ]
D. Cai, Z. Cai
Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations
preprint
- [ link ][ view ]
D. Cai, J. Nagy, and Y. Xi
Fast and Stable Deterministic Approximation of General Symmetric Kernel Matrices in High Dimensions
preprint
- [][] A paper (to be submitted)
- [][] Another paper (to be submitted)
- [][] Reserve your spot (in preparation)
- [][] My research interests are spontaneous (to be rejected)