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The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on…

Markov Random Fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms.…

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…

Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the…

Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both…

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth…

Several variants of Neural Radiance Fields (NeRFs) have significantly improved the accuracy of synthesized images and surface reconstruction of 3D scenes/objects. In all of these methods, a key characteristic is that none can train the…

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…

Sparse-view computed tomography (CT) is a practical solution to reduce radiation dose, but the resulting ill-posed inverse problem poses significant challenges for accurate image reconstruction. Although deep learning and diffusion-based…

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor…

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several…

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards…

One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in…

Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in…

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale…

Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models…

We propose a computationally efficient alternative to generalized random forests (GRFs) for estimating heterogeneous effects in large dimensions. While GRFs rely on a gradient-based splitting criterion, which in large dimensions is…

Super-resolution is an ill-posed problem, since it allows for multiple predictions for a given low-resolution image. This fundamental fact is largely ignored by state-of-the-art deep learning based approaches. These methods instead train a…