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Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field…

In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.

Differential Geometry · Mathematics 2019-06-19 A. V. Gavrilov

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

Machine Learning · Computer Science 2021-10-26 Marin Biloš , Johanna Sommer , Syama Sundar Rangapuram , Tim Januschowski , Stephan Günnemann

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…

Machine Learning · Computer Science 2025-06-05 Raj Ghugare , Benjamin Eysenbach

Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of…

High Energy Physics - Lattice · Physics 2022-07-07 Michele Caselle , Elia Cellini , Alessandro Nada , Marco Panero

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

Machine Learning · Statistics 2016-06-15 Danilo Jimenez Rezende , Shakir Mohamed

Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…

Computational Physics · Physics 2022-08-23 Alessandro Coretti , Sebastian Falkner , Phillip Geissler , Christoph Dellago

We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations.…

Logic · Mathematics 2015-07-01 Alessio Guglielmi , Tom Gundersen

We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our…

Classical Analysis and ODEs · Mathematics 2017-02-06 Antti Käenmäki

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…

Functional Analysis · Mathematics 2007-05-23 Michael Kunzinger , Michael Oberguggenberger , Roland Steinbauer , James A. Vickers

Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…

Dynamical Systems · Mathematics 2017-06-07 Vladislav Kruglov , Dmitry Malyshev , Olga Pochinka

The study of high dimensional data sets often rely on their low dimensional projections that preserve the local geometry of the original space. While numerous methods have been developed to summarize this space as variations of tree-like…

Machine Learning · Computer Science 2023-11-21 Guangzheng Zhang , Bingxian Xu

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…

Machine Learning · Computer Science 2024-04-24 Qinglong Meng , Chongkun Xia , Xueqian Wang

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…

Chaotic Dynamics · Physics 2009-10-31 Weinan E , Eric Vanden Eijnden

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is…

Differential Geometry · Mathematics 2014-07-07 D. H. Phong , Jian Song , Jacob Sturm , Xiaowei Wang

This study focuses on the novel application of a normalizing flow as a method of domain adaptation. Normalizing flows offer a way to transform data points between two different distributions. The present study investigates a method of…

Data Analysis, Statistics and Probability · Physics 2024-05-16 Rowan Kelleher , Anselm Vossen

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model…

Machine Learning · Computer Science 2020-11-02 Didrik Nielsen , Priyank Jaini , Emiel Hoogeboom , Ole Winther , Max Welling

To overcome topological constraints and improve the expressiveness of normalizing flow architectures, Wu, K\"ohler and No\'e introduced stochastic normalizing flows which combine deterministic, learnable flow transformations with stochastic…

Machine Learning · Computer Science 2022-12-02 Paul Hagemann , Johannes Hertrich , Gabriele Steidl

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes…

Differential Geometry · Mathematics 2015-12-08 Hao Yin