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Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…

Fundamental diagrams describe the relationship between speed, flow, and density for some roadway (or set of roadway) configuration(s). These diagrams typically do not reflect, however, information on how speed-flow relationships change as a…

In this study, we use Rational-Quadratic Neural Spline Flows, a sophisticated parametrization of Normalizing Flows, for inferring posterior probability distributions in scenarios where direct evaluation of the likelihood is challenging at…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…

For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…

In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second…

The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…

Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of…

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…

In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…

In this contribution, we introduce a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes. It relies on the stationary action principle and interface geometric variables. The main ideas…

Prior flow matching methods in robotics have primarily learned velocity fields to morph one distribution of trajectories into another. In this work, we extend flow matching to capture second-order trajectory dynamics, incorporating…

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…

Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…

Two-phase flow systems in porous media have complex dynamics. It is well established that a wide range of system parameters like viscosities and porosity as well as flow parameters such as pressure gradient and fluid saturation have strong…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…