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Microstructures, characterized by intricate structures at the microscopic scale, hold the promise of important disruptions in the field of mechanical engineering due to the superior mechanical properties they offer. One fundamental…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…
The inverse design of microstructures plays a pivotal role in optimizing metamaterials with specific, targeted physical properties. While traditional forward design methods are constrained by their inability to explore the vast…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
As details are missing in most representations of structures, the lack of controllability to more information is one of the major weaknesses in structure-based controllable point cloud generation. It is observable that definitions of…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
We present a novel application of neural networks to design improved mixing elements for single-screw extruders. Specifically, we propose to use neural networks in numerical shape optimization to parameterize geometries. Geometry…
Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
Simulation-based approaches to microstructure generation can suffer from a variety of limitations, such as high memory usage, long computational times, and difficulties in generating complex geometries. Generative machine learning models…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
Recently, deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. Although these approaches provide significant performance gain compared to compressed…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is…