Related papers: Discovering Data Manifold Geometry via Non-Contrac…
We propose GeoNet, a jointly unsupervised learning framework for monocular depth, optical flow and ego-motion estimation from videos. The three components are coupled by the nature of 3D scene geometry, jointly learned by our framework in…
We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…
Generative machine learning models have been demonstrated to be able to learn low dimensional representations of data that preserve information required for downstream tasks. In this work, we demonstrate that flow matching based generative…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully…
Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family…
World models compress rich sensory streams into compact latent codes that anticipate future observations. We let separate agents acquire such models from distinct viewpoints of the same environment without any parameter sharing or…
Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific…
We introduce a new global Lagrangian descriptor that is applied to flows with general time dependence (altimetric datasets). It succeeds in detecting simultaneously, with great accuracy, invariant manifolds, hyperbolic and non-hyperbolic…
Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on…
Optical flow estimation is a fundamental problem in computer vision, yet the reliance on expensive ground-truth annotations limits the scalability of supervised approaches. Although unsupervised and semi-supervised methods alleviate this…
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…