  Traditional maximum entropy and sparsity-based algorithms for analytic
continuation often suffer from the ill-posed kernel matrix or demand tremendous
computation time for parameter tuning. Here we propose a neural network method
by convex optimization and replace the ill-posed inverse problem by a sequence
of well-conditioned surrogate problems. After training, the learned optimizers
are able to give a solution of high quality with low time cost and achieve
higher parameter efficiency than heuristic fully-connected networks. The output
can also be used as a neural default model to improve the maximum entropy for
better performance. Our methods may be easily extended to other
high-dimensional inverse problems via large-scale pretraining.
