相关论文: On interpretability and proper latent decompositio…

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form…

Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in…

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…

Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…

The practice of transforming raw data to a feature space so that inference can be performed in that space has been popular for many years. Recently, rapid progress in deep neural networks has given both researchers and practitioners…

Learning useful representations of complex data has been the subject of extensive research for many years. With the diffusion of Deep Neural Networks, Variational Autoencoders have gained lots of attention since they provide an explicit…

We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and…

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise…

Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However,…

It is shown that applying manifold learning techniques to Poincar\'e sections of high-dimensional, chaotic dynamical systems can uncover their low-dimensional topological organization. Manifold learning provides a low-dimensional embedding…

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…

Variational Autoencoder is typically understood from the perspective of probabilistic inference. In this work, we propose a new geometric reinterpretation which complements the probabilistic view and enhances its intuitiveness. We…

Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…

3D geometric contents are becoming increasingly popular. In this paper, we study the problem of analyzing deforming 3D meshes using deep neural networks. Deforming 3D meshes are flexible to represent 3D animation sequences as well as…

Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically…

Unsupervised discovery of latent representations, in addition to being useful for density modeling, visualisation and exploratory data analysis, is also increasingly important for learning features relevant to discriminative tasks.…

Autonomous driving has received a lot of attention in the automotive industry and is often seen as the future of transportation. Passenger vehicles equipped with a wide array of sensors (e.g., cameras, front-facing radars, LiDARs, and IMUs)…

Continuous control over azimuthal flow and shear in the edge of the Large Plasma Device (LAPD) has been achieved using a biasable limiter which has allowed a careful study of the effect of flow shear on pressure-gradient-driven turbulence…

Autoencoders, which consist of an encoder and a decoder, are widely used in machine learning for dimension reduction of high-dimensional data. The encoder embeds the input data manifold into a lower-dimensional latent space, while the…

We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…