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We present VecFusion, a new neural architecture that can generate vector fonts with varying topological structures and precise control point positions. Our approach is a cascaded diffusion model which consists of a raster diffusion model…

In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…

We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we…

A novel volume of fluid model (VoF) called explicit volume diffusion (EVD) is developed for the simulation of interfacial flows, including those with turbulence and primary spray atomisation. The EVD model is derived by volume averaging the…

The autoencoder model uses an encoder to map data samples to a lower dimensional latent space and then a decoder to map the latent space representations back to the data space. Implicitly, it relies on the encoder to approximate the inverse…

Stein variational gradient descent (SVGD) is a kernel-based and non-parametric particle method for sampling from a target distribution, such as in Bayesian inference and other machine learning tasks. Different from other particle methods,…

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on target runout profile. Traditional high-fidelity simulators for these inverse problems are…

This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are…

Super-resolution is widely used in medical imaging to enhance low-quality data, reducing scan time and improving abnormality detection. Conventional super-resolution approaches typically rely on paired datasets of downsampled and original…

We introduce Purrception, a variational flow matching approach for vector-quantized image generation that provides explicit categorical supervision while maintaining continuous transport dynamics. Our method adapts Variational Flow Matching…

Graph diffusion models have recently been proposed to synthesize entire graphs, such as molecule graphs. Although existing methods have shown great performance in generating entire graphs for graph-level learning tasks, no graph diffusion…

Graph Convolutional Networks (GCNs) have attracted more and more attentions in recent years. A typical GCN layer consists of a linear feature propagation step and a nonlinear transformation step. Recent works show that a linear GCN can…

We propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and the flow…

GNNs are widely used to solve various tasks including node classification and link prediction. Most of the GNN architectures assume the initial embedding to be random or generated from popular distributions. These initial embeddings require…

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…

Synthesizing novel views from monocular videos of dynamic scenes remains a challenging problem. Scene-specific methods that optimize 4D representations with explicit motion priors often break down in highly dynamic regions where multi-view…

Recent advances of semantic image segmentation greatly benefit from deeper and larger Convolutional Neural Network (CNN) models. Compared to image segmentation in the wild, properties of both medical images themselves and of existing…

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…