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Computational multiscale modeling encompasses a wide range of end-products and a great number of technological applications. This paper provides an overview of the computational multiscale modeling approach based on the utilization of MBN…
Several visualization schemes have been developed for imaging materials at the atomic level through atom probe tomography. The main shortcoming of these tools is their inability to parallel process data using multi-core computing units to…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
AI-based structural design represents a transformative approach that addresses the inefficiencies inherent in traditional structural design practices. This paper innovates the existing AI-based design frameworks from four aspects and…
This paper presents a comprehensive survey of computational imaging (CI) techniques and their transformative impact on computer vision (CV) applications. Conventional imaging methods often fail to deliver high-fidelity visual data in…
In this article we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology,…
Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
CSG trees are an intuitive, yet powerful technique for the representation of geometry using a combination of Boolean set-operations and geometric primitives. In general, there exists an infinite number of trees all describing the same 3D…
Additive Manufacturing (AM) is a transformative manufacturing technology enabling direct fabrication of complex parts layer-be-layer from 3D modeling data. Among AM applications, the fabrication of Functionally Graded Materials (FGMs) has…
We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the…
The goal of this document is to survey existing methods for recovering CSG representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the…
In the paper, we propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for solving Stokes and Navier-Stokes equations. We start with a detailed explanation of the method for the…
Reverse engineering 3D computer-aided design (CAD) models from images is an important task for many downstream applications including interactive editing, manufacturing, architecture, robotics, etc. The difficulty of the task lies in vast…
Multimodal learning plays a pivotal role in advancing artificial intelligence systems by incorporating information from multiple modalities to build a more comprehensive representation. Despite its importance, current state-of-the-art…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…
This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation requires…
The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the…