Inspired by DAS-PINNs [1], we try another generative model instead of KR net [2] (a kind of flow-based model) as used in [1] based on optimal transport, which was proposed in AE-OT [3], to cope with the PDE problem with complex boundaries.
It seems that KR net (maybe most of flow-based models) does not work perfectly well when the support set of the probability distribution to be learned is too complex (i.e. the support set is not simply connected).
We create a pytorch version of KR net. And we try the problem with 2 peaks in DAS-PINNs [1] using both KR net and AE-OT generative model.
pytorch >= 2.1 ( previous versions may work as well )
DAS-PINNs: https://github.com/MJfadeaway/DAS
AE-OT: https://github.com/k2cu8/pyOMT
[1] Tang K, Wan X, Yang C. DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations[J]. Journal of Computational Physics, 2023, 476: 111868.
[2] Tang K, Wan X, Liao Q. Adaptive deep density approximation for Fokker-Planck equations[J]. Journal of Computational Physics, 2022, 457: 111080.
[3] An D, Guo Y, Lei N, et al. AE-OT: A new generative model based on extended semi-discrete optimal transport[J]. ICLR 2020, 2019.
samples using generative model in AE-OT (green)
error
