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Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this…
Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the…
From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM), that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces.…
Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
We present a high-fidelity three dimensional computational framework for simulating the bulk mechanical behavior of granular aggregates composed of deformable brittle grains. Departing from classical discrete element methods (DEM), our…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
This study presents and calibrates a Discrete Element Method (DEM) contact model for wet granular materials in the pendular regime. The model extends a previously calibrated dry contact formulation by incorporating liquid bridges that…
Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…
This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…
Generative models of graphs based on discrete Denoising Diffusion Probabilistic Models (DDPMs) offer a principled approach to molecular generation by systematically removing structural noise through iterative atom and bond adjustments.…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
Computational fluid dynamics and discrete element method (CFD-DEM) coupling is an efficient and powerful tool to simulate particle-fluid systems. However, current volume-averaged CFD-DEM relying on direct grid-based mapping between the…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
The recently developed level-set-DEM is able to seamlessly handle arbitrarily shaped grains and their contacts through a discrete level-set representation of grains' volume and a node-based discretization of their bounding surfaces.…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the…