Related papers: Geometric Meta-Learning via Coupled Ricci Flow: Un…

This work presents DCFlow, a novel unsupervised cross-modal flow estimation framework that integrates a decoupled optimization strategy and a cross-modal consistency constraint. Unlike previous approaches that implicitly learn flow…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…

In this paper we characterize non-collapsed limits of Ricci flows. We show that such limits are smooth away from a set of codimension $\geq 4$ in the parabolic sense and that the tangent flows at every point are given by gradient shrinking…

Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…

Open-vocabulary panoptic reconstruction is essential for advanced robotics perception and simulation. However, existing methods based on 3D Gaussian Splatting (3DGS) often struggle to simultaneously achieve geometric accuracy, coherent…

The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our recent work where sectoriality for the generator of the…

Hypergraph neural networks (HGNNs) have demonstrated strong capabilities in modeling complex higher-order relationships. However, existing HGNNs often suffer from over-smoothing as the number of layers increases and lack effective control…

Let ${\bf M}$ be a compact Riemannian manifold and the metrics $g=g(t)$ evolve by the Ricci flow. We prove the following result. The Sobolev imbedding by Aubin or Hebey, perturbed by a scalar curvature term and modulo sharpness of…

This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction.…

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this…

Ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes. This idea has been around…

In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence…

Relative Geologic Time (RGT) estimation from seismic data is a cornerstone of subsurface structural modeling, depositional evolution analysis, and reservoir characterization, supporting horizon correlation and depositional system…

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain…

Relativistic hydrodynamics is a powerful tool to simulate the evolution of the quark gluon plasma (QGP) in relativistic heavy ion collisions. Using 10000 initial and final profiles generated from 2+1-d relativistic hydrodynamics VISH2+1…

LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…