Related papers: Tensor Gauge Flow Models
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a…
Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…
We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven…
We introduce an entirely new class of high-order methods for computational fluid dynamics (CFD) based on the Gaussian Process (GP) family of stochastic functions. Our approach is to use kernel-based GP prediction methods to…
As a probabilistic modeling technique, the flow-based model has demonstrated remarkable potential in the field of lossless compression \cite{idf,idf++,lbb,ivpf,iflow},. Compared with other deep generative models (eg. Autoregressive, VAEs)…
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the…
Tabular regression is a well-studied problem with numerous industrial applications, yet most existing approaches focus on point estimation, often leading to overconfident predictions. This issue is particularly critical in industrial…
Normalizing flows are a powerful class of generative models demonstrating strong performance in several speech and vision problems. In contrast to other generative models, normalizing flows are latent variable models with tractable…
Traffic flow prediction plays an important role in Intelligent Transportation Systems in traffic management and urban planning. There have been extensive successful works in this area. However, these approaches focus only on modelling the…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a…
Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…