Related papers: Discovering Symmetry Groups with Flow Matching
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
Scene flow is the dense 3D reconstruction of motion and geometry of a scene. Most state-of-the-art methods use a pair of stereo images as input for full scene reconstruction. These methods depend a lot on the quality of the RGB images and…
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or…
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…
Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of…
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…
Diffusion models can learn rich representations during data generation, showing potential for Self-Supervised Learning (SSL), but they face a trade-off between generative quality and discriminative performance. Their iterative sampling also…
Discovering new solid-state materials requires rapidly exploring the vast space of crystal structures and locating stable regions. Generating stable materials with desired properties and compositions is extremely difficult as we search for…
Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…
LiDAR scene flow is the task of estimating per-point 3D motion between consecutive point clouds. Recent methods achieve centimeter-level accuracy on popular autonomous vehicle (AV) datasets, but are typically only trained and evaluated on a…
We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…
Sewing patterns define the structural foundation of garments and are essential for applications such as fashion design, fabrication, and physical simulation. Despite progress in automated pattern generation, accurately modeling sewing…
In optical flow estimation task, coarse-to-fine (C2F) warping strategy is widely used to deal with the large displacement problem and provides efficiency and speed. However, limited by the small search range between the first images and…
We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…
In this paper, we study the Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions of the system. The infinitesimal generators that span the Lie algebra for this…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…