Related papers: Atlas flow : compatible local structures on the ma…

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…

We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a…

We propose the joint graph attention neural network (GAT), clustering with adaptive neighbors (CAN) and probabilistic graphical model for dynamic power flow analysis and fault characteristics. In fact, computational efficiency is the main…

Generative Adversarial Networks (GANs) can synthesize realistic images, with the learned latent space shown to encode rich semantic information with various interpretable directions. However, due to the unstructured nature of the learned…

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by artificial neural network (ANN) based on the local coordinate system…

We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in…

Graph neural networks (GNNs) excel on homophilic graphs where connected nodes share labels, but struggle with heterophilic graphs where edges do not imply similarity. Moreover, iterative message passing limits scalability due to…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…

Flow-matching generative models are increasingly used to simulate cell responses to biological perturbations. However, the design space for building such models is large and underexplored. We systematically analyse the design space of flow…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

Simulating urban morphology with location attributes is a challenging task in urban science. Recent studies have shown that Generative Adversarial Networks (GANs) have the potential to shed light on this task. However, existing GAN-based…

Generative Adversarial Networks (GANs) with style-based generators (e.g. StyleGAN) successfully enable semantic control over image synthesis, and recent studies have also revealed that interpretable image translations could be obtained by…

Work considers the usage of StyleGAN architecture for the task of microstructure synthesis. The task is the following: given number of samples of structure we try to generate similar samples at the same time preserving its properties. Since…

We present a framework for efficiently approximating differential-geometric primitives on arbitrary manifolds via construction of an atlas graph representation, which leverages the canonical characterization of a manifold as a finite…

Many generative applications, such as synthesis-based 3D molecular design, involve constructing compositional objects with continuous features. Here, we introduce Compositional Generative Flows (CGFlow), a novel framework that extends flow…

Approximating wind flows using computational fluid dynamics (CFD) methods can be time-consuming. Creating a tool for interactively designing prototypes while observing the wind flow change requires simpler models to simulate faster. Instead…

Topology-consistent dynamic model sequences are essential for applications such as animation and model editing. However, existing 4D reconstruction methods face challenges in generating high-quality topology-consistent meshes. To address…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

Existing dominant methods for audio generation include Generative Adversarial Networks (GANs) and diffusion-based methods like Flow Matching. GANs suffer from slow convergence during training, while diffusion methods require multi-step…