NSF DMS-2110571

**Publications**

- (with M. Liu)
*Self-adaptive ReLU neural network method in least-squares data fitting*, Handbook of Research in Adaptive Artificial Intelligence, submitted. - (with J. Chen and M. Liu)
*Self-adaptive deep neural network: numerical approximation to functions and PDEs*,*J. Comput. Phys.*, 455 (2022), 111021. - (with M. Liu)
*Adaptive two-layer ReLU neural network: II. RITZ approximation to elliptic PDEs*,*Comput. Math. Appl.*, 113 (2022), 103-116. - (with M. Liu and J. Chen)
*Adaptive two-layer ReLU neural network: I. Best least-squares approximation*,*Comput. Math. Appl.*, 113 (2022), 34-44. - (with J. Choi and M. Liu)
*Least-squares neural network (LSNN) method for linear advection-reaction equation: non-constant jumps*, submitted. - (with J. Choi and M. Liu)
*Least-squares neural network (LSNN) method for linear advection-reaction equation: general discontinuous interface*,*arXiv:2301.06156v3[math.NA]*. - (with J. Chen and M. Liu)
*Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator*,*arXiv2110.10895v3[math.NA]*,*J. Comput. Appl. Math.*, 433 (2023) 115298. - (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 J. Chen and M. Liu)
*Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation*,*J. Comput. Phys.*, 443 (2021), 110514. - (with M. Liu and K. Ramani)
*Deep Ritz method with adaptive quadrature for linear elasticity*,*Comput. Methods in Appl. Mech. Eng.*,*415 (2023) 116229*. - (with D. Jiao and M. Liu)
*Minimization formulation for neural network based solution of Maxwell's equations in frequency domain*,*in the IEEE International Symposium on Antennas & Propagation, USNC-URSI Radio Science Meeting*, July 10-15, 2022, Denver, USA. - (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.

**Adaptive Neural Network (ANE) Method**

**Least-Squares Neural Network (LSNN) Method**

**Deep Ritz Method**

*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.