140 citations · 153 across the 2 of their papers we have counts for
6 papers
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
Beichuan Deng, Yeonjong Shin, Lu Lu +2
We present convergence analysis of operator learning in [Chen and Chen 1995] and [Lu et al. 2020], where continuous operators are approximated by a sum of products of branch and tr…
Operator learning for predicting multiscale bubble growth dynamics
Chensen Lin, Zhen Li, Lu Lu +3
Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investiga…
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks
Shengze Cai, Zhicheng Wang, Lu Lu +2
Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengt…
Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis +1
In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials a…
Dying ReLU and Initialization: Theory and Numerical Examples
Lu Lu, Yeonjong Shin, Yanhui Su +1
The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die.…
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Dongkun Zhang, Lu Lu, Ling Guo +1
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids,…