Related papers: Global Optimization methods for Gravitational Lens…
The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…
In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…
We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Strong gravitational lensing is a powerful tool for probing the nature of dark matter, as lensing signals are sensitive to the dark matter substructure within the lensing galaxy. We present a comparative analysis of strong gravitational…
We present a new pixelized method for the inversion of gravitationally lensed extended source images which we term adaptive semi-linear inversion (SLI). At the heart of the method is an h-means clustering algorithm which is used to derive a…
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…
In the era of large-scale astronomical surveys, fast modeling of strong lens systems has become increasingly vital. While significant progress has been made for galaxy-scale lenses, the development of automated methods for modeling larger…
Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
We develop regularization methods to find flat minima while training deep neural networks. These minima generalize better than sharp minima, yielding models outperforming baselines on real-world test data (which may be distributed…
Galactic sized gravitational lenses are simulated by combining a cosmological N-body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated…
We present a machine learning method for the reconstruction of the undistorted images of background sources in strongly lensed systems. This method treats the source as a pixelated image and utilizes the Recurrent Inference Machine (RIM) to…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
This paper presents an adaptive sampling algorithm tailored for the optimization of parametrized dynamical systems using projection-based model order reduction. Unlike classical sampling strategies, this framework does not aim for a small…
In statistics, it is common to encounter multi-modal and non-smooth likelihood (or objective function) maximization problems, where the parameters have known upper and lower bounds. This paper proposes a novel derivative-free global…
This paper presents a new complex optimization problem in the field of automatic design of advanced industrial systems and proposes a hybrid optimization approach to solve the problem. The problem is multi-objective as it aims at finding…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…