Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction

We present a novel offline-online method to mitigate the computational burden of characterization posterior random variables in statistical learning. In offline phase, proposed learns joint law parameter and observable tensor-train (TT) format. online resulting order-preserving conditional transport can characterize given newly observed data real time. Compared with state-of-the-art normalizing flow techniques, relies on function approximation is equipped thorough performance analysis. The perspective also allows us further extend capability maps challenging problems high-dimensional observations parameters. On one hand, we heuristics reorder and/or reparametrize enhance power TT. other integrate TT-based reordering/reparametrization into layered compositions improve maps. demonstrate efficiency various learning tasks ordinary differential equations (ODEs) partial (PDEs).