Publications

Adaptive Neural Network (ANE) Method

1. (with M. Liu) Self-adaptive ReLU neural network method in least-squares data fitting, Handbook of Research in Adaptive Artificial Intelligence, submitted.
2. (with J. Chen and M. Liu) Self-adaptive deep neural network: numerical approximation to functions and PDEs, J. Comput. Phys., 455 (2022), 111021.
3. (with M. Liu) Adaptive two-layer ReLU neural network: II. RITZ approximation to elliptic PDEs, Comput. Math. Appl., 113 (2022), 103-116.
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.

Least-Squares Neural Network (LSNN) Method

5. (with J. Choi and M. Liu) Least-squares neural network (LSNN) method for linear advection-reaction equation: non-constant jumps, submitted.
6. (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].
7. (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.
8. (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.
9. (with J. Chen and M. Liu) Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation, J. Comput. Phys., 443 (2021), 110514.

Deep Ritz Method

10. (with M. Liu and K. Ramani) Deep Ritz method with adaptive quadrature for linear elasticity, Comput. Methods in Appl. Mech. Eng., 415 (2023) 116229.
11. (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.
12. (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.

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.