Related papers: Machine learning on manifolds for inverse scatteri…
A black-box spectral method is introduced for evaluating the adversarial robustness of a given machine learning (ML) model. Our approach, named SPADE, exploits bijective distance mapping between the input/output graphs constructed for…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…
Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and…
Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values.…
Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Although it is known that having accurate Lipschitz estimates is essential for certain models to deliver good predictive performance, refining this constant in practice can be a difficult task especially when the input dimension is high. In…
We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems…
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…