Related papers: A Density Consistency approach to the inverse Isin…

A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…

This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground-state density matrix is a fixed-point of the DMET map for…

We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

Recently, dense contrastive learning has shown superior performance on dense prediction tasks compared to instance-level contrastive learning. Despite its supremacy, the properties of dense contrastive representations have not yet been…

Materials with heterogeneous structures exhibit complex physical processes such as delamination, cracks, and plasticity, which require micromechanical parameters for understanding. However, identifying these parameters is challenging due to…

Contrastive learning is a recent promising approach in unsupervised representation learning where a feature representation of data is learned by solving a pseudo classification problem from unlabelled data. However, it is not…

In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares…

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

In this paper, a novel model-based distributed compressive sensing (DCS) algorithm is proposed. DCS exploits the inter-signal correlations and has the capability to jointly recover multiple sparse signals. Proposed approach is a Bayesian…

The increasing computational requirements of deep neural networks (DNNs) have led to significant interest in obtaining DNN models that are sparse, yet accurate. Recent work has investigated the even harder case of sparse training, where the…

We investigate the thermodynamic and critical properties of an interacting domain wall model which is derived from the triangular lattice antiferromagnetic Ising model with the anisotropic nearest and next nearest neighbor interactions. The…

Nowadays massive amount of data are available for analysis in natural and social systems. Inferring system structures from the data, i.e., the inverse problem, has become one of the central issues in many disciplines and interdisciplinary…

Bound-to-Bound Data Collaboration (B2BDC) provides a natural framework for addressing both forward and inverse uncertainty quantification problems. In this approach, QOI (quantity of interest) models are constrained by related experimental…

We present an exact analytical solution for the one-dimensional Ising model in the presence of an external magnetic field applied periodically to every $k$-th site. The problem is handled using the symmetrized transfer matrix approach, we…

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…