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Deep learning has received extensive research interest in developing new medical image processing algorithms, and deep learning based models have been remarkably successful in a variety of medical imaging tasks to support disease detection…

We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…

This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian…

Many statistical models have high accuracy on test benchmarks, but are not explainable, struggle in low-resource scenarios, cannot be reused for multiple tasks, and cannot easily integrate domain expertise. These factors limit their use,…

The small world of matter is getting smaller and smaller. Nano sciences in recent years had huge developments allowing nanotechnologies to take enormous steps in the development of materials and processes. Numerous applications in a wide…

We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…

Over the course of the recent decade, tremendous progress has been made in the areas of machine learning and natural language processing, which opened up vast areas of potential application use cases, including hiring and human resource…

This extended abstract is based on a talk given at the workshop and summer school ``Direct and Inverse Problems with Applications" in Ghent Analysis and PDE Centre in August 2024. It focuses on nonlinear diffusion equations of slow and fast…

The microservices architectural style is widely favored for its scalability, reusability, and easy maintainability, prompting increased adoption by developers. However, transitioning from a monolithic to a microservices-based architecture…

These are the lecture notes for the summer course given for 2018 Mathematical Finance Summer School at Shandong Unversity. It contains a brief introduction to the Kyle model and the related topics in filtering, enlargement of filtrations…

The ability to deploy neural networks in real-world, safety-critical systems is severely limited by the presence of adversarial examples: slightly perturbed inputs that are misclassified by the network. In recent years, several techniques…

Through this project, we researched on transfer learning methods and their applications on real world problems. By implementing and modifying various methods in transfer learning for our problem, we obtained an insight in the advantages and…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…

We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a…

Magnetic data inversion is an important tool in geophysics, used to infer subsurface magnetic susceptibility distributions from surface magnetic field measurements. This inverse problem is inherently ill-posed, characterized by non-unique…

Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for…

This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…