Energy stable neural network for gradient flow equations
Ganghua Fan Tianyu Jin Yuan Lan Yang Xiang Luchan Zhang
In this paper, we propose an energy stable network (EStable-Net) for solving
gradient flow equations. The solution update scheme in our neural network
EStable-Net is inspired by a proposed auxiliary variable based equivalent form
of the gradient flow equation. EStable-Net enables decreasing of a discrete
energy along the neural network, which is consistent with the property in the
evolution process of the gradient flow equation. The architecture of the neural
network EStable-Net consists of a few energy decay blocks, and the output of
each block can be interpreted as an intermediate state of the evolution process
of the gradient flow equation. This design provides a stable, efficient and
interpretable network structure. Numerical experimental results demonstrate
that our network is able to generate high accuracy and stable predictions.