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math.AP2021★ 13 cited
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…
math.AP2018
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,…