270 citations · 660 across the 46 of their papers we have counts for
47 papers
Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
Guanhang Lei, Zhen Lei, Lei Shi +2
Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some r…
Energy transfer and radiation in Hamiltonian nonlinear Klein-Gordon equations: general case
Zhen Lei, Jie Liu, Zhaojie Yang
In this paper, we consider Klein-Gordon equations with cubic nonlinearity in three spatial dimensions, which are Hamiltonian perturbations of the linear one with potential. It is a…
Quantitative partial regularity of the Navier-Stokes equations and applications
Zhen Lei, Xiao Ren
We prove a logarithmic improvement of the Caffarelli-Kohn-Nirenberg partial regularity theorem for the Navier-Stokes equations. The key idea is to find a quantitative counterpart f…
Solving parametric partial differential equations with deep rectified quadratic unit neural networks
Zhen Lei, Lei Shi, Chenyu Zeng
Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient than using many conventional num…
Radiation of the energy-critical wave equation with compact support
Zhen Lei, Xiao Ren, Zhaojie Yang
We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions , with compactly supported initial…
The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded
Shijie Dong, Philippe G. LeFloch, Zhen Lei
Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time…