Related papers: Variational Flow Models: Flowing in Your Style

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…

A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave…

We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…

In recent years, diffusion-based generative models have demonstrated remarkable performance in speech conversion, including Denoising Diffusion Probabilistic Models (DDPM) and others. However, the advantages of these models come at the cost…

We propose a data-driven viscosity solver based on U-shaped convolutional neural network to predict velocity changes due to viscosity. Our solver takes velocity derivatives, fluid volume, and solid indicator quantities as input. The…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce spectral flow learning, which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman…

Steady-state process models are common in virtual flow meter applications due to low computational complexity, and low model development and maintenance cost. Nevertheless, the prediction performance of steady-state models typically…

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…

We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ…

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…

Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative…

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly…

Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

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…

We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…