Short-fiber-reinforced composites (SFRC) are high-performance engineering
materials for lightweight structural applications in the automotive and
electronics industries. Typically, SFRC structures are manufactured by
injection molding, which induces heterogeneous microstructures, and the
resulting nonlinear anisotropic behaviors are challenging to predict by
conventional micromechanical analyses. In this work, we present a machine
learning-based multiscale method by integrating injection molding-induced
microstructures, material homogenization, and Deep Material Network (DMN) in
the finite element simulation software LS-DYNA for structural analysis of SFRC.
DMN is a physics-embedded machine learning model that learns the microscale
material morphologies hidden in representative volume elements of composites
through offline training. By coupling DMN with finite elements, we have
developed a highly accurate and efficient data-driven approach, which predicts
nonlinear behaviors of composite materials and structures at a computational
speed orders-of-magnitude faster than the high-fidelity direct numerical
simulation. To model industrial-scale SFRC products, transfer learning is
utilized to generate a unified DMN database, which effectively captures the
effects of injection molding-induced fiber orientations and volume fractions on
the overall composite properties. Numerical examples are presented to
demonstrate the promising performance of this LS-DYNA machine learning-based
multiscale method for SFRC modeling.

本研究提出了一种基于机器学习的多尺度方法，将注射成型引起的微观结构，材料均质化和深度材料网络（DMN）与有限元模拟软件 LS-DYNA 相结合，用于短纤维增强复合材料的结构分析。通过将 DMN 与有限元耦合，我们开发了一种高度准确和高效的数据驱动方法，该方法以比高保真度直接数值模拟快若干个数量级的计算速度预测复合材料和结构的非线性行为。

基于 LS-DYNA 机器学习的短纤维增强复合材料非线性建模的多尺度方法

LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Composites

Detecting edges is a fundamental problem in computer vision with many
applications, some involving very noisy images. While most edge detection
methods are fast, they perform well only on relatively clean images. Indeed,
edges in such images can be reliably detected using only local filters.
Detecting faint edges under high levels of noise cannot be done locally at the
individual pixel level, and requires more sophisticated global processing.
Unfortunately, existing methods that achieve this goal are quite slow. In this
paper we develop a novel multiscale method to detect curved edges in noisy
images. While our algorithm searches for edges over a huge set of candidate
curves, it does so in a practical runtime, nearly linear in the total number of
image pixels. As we demonstrate experimentally, our algorithm is orders of
magnitude faster than previous methods designed to deal with high noise levels.
Nevertheless, it obtains comparable, if not better, edge detection quality on a
variety of challenging noisy images.

本文提出了一种新的多尺度方法来检测嘈杂图像中的曲线边缘，算法基于候选曲线，针对高噪声情况进行全局处理，实现了较快的运行时间，同时在各种具有挑战性的嘈杂图像上获得了可比较甚至更好的边缘检测质量。

低信噪比下曲线边缘的快速检测

Fast Detection of Curved Edges at Low SNR

Persistent homology is a multiscale method for analyzing the shape of sets
and functions from point cloud data arising from an unknown distribution
supported on those sets. When the size of the sample is large, direct
computation of the persistent homology is prohibitive due to the combinatorial
nature of the existing algorithms. We propose to compute the persistent
homology of several subsamples of the data and then combine the resulting
estimates. We study the risk of two estimators and we prove that the
subsampling approach carries stable topological information while achieving a
great reduction in computational complexity.

本文提出了一种结合多样本子采样进行计算的持久性同调计算方法，证明该方法具有稳定的拓扑信息和较小的计算复杂度。