Learned SVD: solving inverse problems via hybrid autoencoding
This work addresses inverse problems in physics-driven data for researchers and practitioners, offering a hybrid method that is incremental in combining model-based and data-driven techniques.
The paper tackles the problem of solving inverse problems with incomplete or complex physics by proposing a learned singular value decomposition (L-SVD) that combines autoencoders to learn mappings between signals and measurements. It shows improved performance over classical methods and better interpretability than black-box approaches, though no concrete numbers are provided.
Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular value decomposition (L-SVD), which combines autoencoders that simultaneously learn and connect latent codes for desired signals and given measurements. We provide a convergence analysis for a specifically structured L-SVD that acts as a regularisation method. In a more general setting, we investigate the topic of model reduction via data dimensionality reduction to obtain a regularised inversion. We present a promising direction for solving inverse problems in cases where the underlying physics are not fully understood or have very complex behaviour. We show that the building blocks of learned inversion maps can be obtained automatically, with improved performance upon classical methods and better interpretability than black-box methods.