相关论文: Applications of microlocal analysis to inverse pro…

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

Incidents in microservice environments can be costly and challenging to recover from due to their complexity and distributed nature. Recent advancements in artificial intelligence (AI) offer promising solutions for improving incident…

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

In this paper we cover a few topics on how to treat inverse problems. There are two different flows of ideas. One approach is based on Morse Lemma. The other is based on analyticity which proves that the number of solutions to the inverse…

These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…

The short Communication based on results of notes: Andre Geim "When lost in a multiverse" (Nat. Phys. 13, 1142 (2017)) and Klaus von Klitzing "Metrology in 2019" (Nat. Phys. 13, 198 (2017))

These are lecture notes for a mini-course given at the St. Petersburg School in Probability and Statistical Physics in June 2012. Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov…

Ongoing microlensing surveys have already yielded more than five hundred microlensing events, most of which have been identified in real-time. In this review I present the basic theory and observational status of these surveys. I highlight…

In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…

In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.

In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…

This mini-review provides a perspective on recent progress and emerging directions aimed at utilizing and controlling in-plane optical polarization, highlighting key application spaces where in-plane near-field tip responses have enabled…

This is a survey lecture note on the applications of Langlands functoriality which were obtained recently by some people at the Langalnds school. This lecture was delivered at the Department of Mathematics, Kyoto University, Japan on June…

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

Recent work demonstrated that flow-based invertible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible architectures and related models fare on two intuitive,…

This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.

This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…

In the inverse problem in particle physics, given an unexpected observation, one aims to identify a unique choice from amongst several competing hypotheses. We explore a novel approach of applying self-organizing maps to the inverse problem…

This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations.…