Learned Optimizers for Analytic Continuation
This addresses computational bottlenecks in physics for analytic continuation, with potential extensions to other high-dimensional inverse problems, though it appears incremental as it builds on existing neural network and optimization techniques.
The paper tackles the problem of analytic continuation in physics, where traditional methods suffer from ill-posed kernel matrices or high computational costs, by proposing a neural network method using convex optimization to replace the inverse problem with well-conditioned surrogate problems. The result is a learned optimizer that provides high-quality solutions with low time cost and higher parameter efficiency than heuristic fully-connected networks, and can also improve maximum entropy methods.
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.