Learning mean curvature-based regularization to solve the inverse variational problems from noisy data

As an emerging mathematical tool, inverse variational problem approximation (IVPA) has some real applications. Recently, deep learning is used to detect physical phenomena and carry out various tasks, which has achieved promising results. Several works have shown that can learn inverse variational problems (IVPs). In this work, we proposed a new framework to solve mean-curvature-based regularization IVPs from noisy data with different levels based on physical constrained learning and automatic differentiation. Furthermore, traditional variational methods and neural networks-based approaches are integrated, to learn the non-convex and high nonlinear inverse variational problems. And several experiments show that the effectiveness and robustness of our algorithm.