Publications

1. (with J. Chen and M. Liu) Finite volume least-squares neural network (FV-LSNN) method for scalar nonlinear hyperbolic conservation laws, arXiv:2110.10895 [math.NA].
2. (with J. Chen and M. Liu) Self-adaptive deep neural network: numerical approximation to functions and PDEs, J. Comput. Phys., 455 (2022), 111021. Free Access before March 31, 2022.
3. (with M. Liu) Adaptive two-layer ReLU neural network: II. RITZ approximation to elliptic PDEs, Comput. Math. Appl., 113 (2022), 103-116. Free Access before May 07, 2022.
4. (with M. Liu and J. Chen) Adaptive two-layer ReLU neural network: I. Best least-squares approximation, Comput. Math. Appl., 113 (2022), 34-44. Free Access before May 06, 2022.
5. (with J. Chen and M. Liu) Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law, Appl. Numer. Math., 174 (2022), 163-176.
6. (with M. Liu and D. Jiao) Ritz neural network (RitzNN) method for H(curl) problems, in the Applied Computational Electromagnetics Society (ACES) Virtual Conference, August 1-5, 2021, ACES2021OL-1302.
7. (with J. Chen and M. Liu) Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation, J. Comput. Phys., 443 (2021), 110514.

1. Neural Nets and Numerical PDEs, Brown University (09/17/21), University of Southern Carolina (10/22/21), Nanjing Normal University, China (03/04/22), ExxonMobil (04/28/22), Xinjiang University, China (05/03/22), Xi'an Jiaotong University, China (10/17/22), Tsinghua University, China (11/03/22)
2. LSNN method for scalar hyperbolic conservation laws, Workshop on Minimum Residual & Least-Squares Finite Element Methods, Oct. 5-7, 2022, Santiago, Chile.