Preconditioned training of normalizing flows for variational inference in inverse problems
This work provides a method to accelerate variational inference for inverse problems with expensive forward operators, which is beneficial for researchers and practitioners in fields like geophysics.
This paper addresses the challenge of sampling from posterior distributions in inverse problems with expensive forward operators, particularly for strongly heterogeneous Earth models. They propose a preconditioning scheme using a conditional normalizing flow (NF) to sample from a low-fidelity posterior, which then accelerates the training of a high-fidelity NF. Numerical experiments show considerable speed-ups compared to training NFs from scratch.
Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.