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.

翻译：本文提出了一种用于求解梯度流方程的能量稳定网络（EStable-Net）。该神经网络中的解更新方案受梯度流方程基于辅助变量的等价形式启发。EStable-Net能够实现沿神经网络的离散能量递减，这一特性与梯度流方程演化过程中的性质相一致。该神经网络EStable-Net的结构由若干能量衰减模块组成，每个模块的输出可解释为梯度流方程演化过程中的一个中间状态。这种设计提供了一种稳定、高效且可解释的网络结构。数值实验结果表明，我们的网络能够生成高精度且稳定的预测结果。