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Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…
Convolutional networks have been extremely successful for regular data structures such as 2D images and 3D voxel grids. The transposition to meshes is, however, not straight-forward due to their irregular structure. We explore how the dual,…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…
Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
A popular testbed for deep learning has been multimodal recognition of human activity or gesture involving diverse inputs such as video, audio, skeletal pose and depth images. Deep learning architectures have excelled on such problems due…
Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative…
In nanoscale, motion operation of a nano-objective is usually realized by displacement load, which put forwards high requirement for ductility of material. Since pristine graphene has low ductility, once the stretching strain exceeds its…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically…
Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…
Factors such as the proliferation of renewable energy and electrification contribute to grid congestion as a pressing problem. Topology control is an appealing method for relieving congestion, but traditional approaches for topology…
The interfacial diffusion associated with finite volume method (FVM) discretizations of multiphase flows creates the need for an interface sharpening mechanism. Such solutions for structured quadrilateral grids are well documented, but…
This paper focuses on addressing challenges posed by non-homogeneous unstructured grids, commonly used in Computational Fluid Dynamics (CFD). Their prevalence in CFD scenarios has motivated the exploration of innovative approaches for…
We advertise the use of tetrahedral grids constructed via the longest edge bisection algorithm for rendering volumetric data with path tracing. The key benefits of such grids is two-fold. First, they provide a highly adaptive…