Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural
  Networks
Chaoyu Liu Zhonghua Qiao Chao Li Carola-Bibiane Schönlieb
This paper proposes a novel approach to integrating partial differential
equation (PDE)-based evolution models into neural networks through a new type
of regularization. Specifically, we propose inverse evolution layers (IELs)
based on evolution equations. These layers can achieve specific regularization
objectives and endow neural networks' outputs with corresponding properties of
the evolution models. Moreover, IELs are straightforward to construct and
implement, and can be easily designed for various physical evolutions and
neural networks. Additionally, the design process for these layers can provide
neural networks with intuitive and mathematical interpretability, thus
enhancing the transparency and explainability of the approach. To demonstrate
the effectiveness, efficiency, and simplicity of our approach, we present an
example of endowing semantic segmentation models with the smoothness property
based on the heat diffusion model. To achieve this goal, we design
heat-diffusion IELs and apply them to address the challenge of semantic
segmentation with noisy labels. The experimental results demonstrate that the
heat-diffusion IELs can effectively mitigate the overfitting problem caused by
noisy labels.