NSF DMS-2110571

**Publications**

- (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]*. - (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*. - (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*. - (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*. - (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. - (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. - (with J. Chen and M. Liu)
*Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation*,*J. Comput. Phys.*, 443 (2021), 110514.

*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)-
*LSNN method for scalar hyperbolic conservation laws*, Workshop on Minimum Residual & Least-Squares Finite Element Methods, Oct. 5-7, 2022, Santiago, Chile.