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Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and…
Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the…
Can standard continuous-time generative models represent distributions whose support is an extremely sparse, globally constrained discrete set? We study this question using completed Sudoku grids as a controlled testbed, treating them as a…
Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…
This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…
Random walk-based node embedding algorithms have attracted a lot of attention due to their scalability and ease of implementation. Previous research has focused on different walk strategies, optimization objectives, and embedding learning…
We measure the energy levels of the excitations of the flux tube between static quark and antiquark in three-dimensional SU(2) gauge theory. Combining exponential error reduction techniques and a variational method we are able to reduce the…
Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…
Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…
Stochastic Gumbel graph networks are proposed to learn high-dimensional time series, where the observed dimensions are often spatially correlated. To that end, the observed randomness and spatial-correlations are captured by learning the…
Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open…
The effective string describing the large distance behaviour of the quark sources of gauge field theories in the confining phase in D=3 or D=4 space-time dimensions can be formulated, in the infrared limit, as a suitable 2D conformal field…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
Normalizing flows are an established approach for modelling complex probability densities through invertible transformations from a base distribution. However, the accuracy with which the target distribution can be captured by the…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…
We consider conserved currents in an interacting network of one-dimensional objects (or strings). Singular currents localized on a single string are considered in general, and a formal procedure for coarse-graining over many strings is…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…