Abstract We consider abstract inverse problems between infinite-dimensional Banach spaces. These are typically nonlinear and ill-posed, making the inversion with limited noisy measurements a delicate process. In this work, we assume that unknown belongs to finite-dimensional manifold: assumption arises in many real-world scenarios where natural objects have low intrinsic dimension belong certai...

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven be a very fruitful idea. The successes this approach have motivated line research into incorporating other symmetries deep learning methods, form group equivariant networks. Much work been focused on roto-translational symmetry $\mathbf R^d$, but examples are sc...

Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these inverse problems, observed multivariate time series used to infer parameters of physical or biological interests. Traditional solutions for often ignore the spatial temporal correlations data (static model), simply model summarized over (time-averaged model). either case...

this paper presents a hybrid technique for simultaneous estimation of parameter and function in inverse heat conduction problems. no prior information is used for the functional form of the heat flux in the present study. the scheme presented here is a combination of two different classical methods: the variable metric method (vmm) and gauss method (gm). the determination of the unknown thermal...

In this paper, we consider some statistical aspects of inverse problems. using Bayesian analysis, particularly estimation and hypothesis-testing questions for parameterdependent differential equations. We relate Bayesian maximum likelihood Io Tikhonw regularization. and we apply the expectatian-minimization (F-M) algorithm to the problem of setting regularization levels. Further, we compare Bay...