The development of machine learning (ML) applications in deep drawing is hindered by limited data availability and the absence of open-access benchmarks for validating novel approaches, including domain generalization over distinct geometries. This paper addresses these challenges by introducing a comprehensive U-shaped dataset tailored to this manufacturing process. Our U-Channel sheet metal (UCSM) dataset combines 90 real-world meshes with an infinite number of synthetic geometry samples generated from four parametric Computer-Aided Design (CAD) models, ensuring extensive geometry variety and data quantity. Additionally, a ready-to-use dataset for drawability assessment and segmentation is provided. Leveraging CAD and mesh data sources bridges the gap between sparse data availability and ML requirements. Our analysis demonstrates that the proposed parametric models are geometrically valid, and real-world and synthetic data complement each other effectively, providing robust support for ML model development. While the dataset is confined to U-shaped, thin-walled, deep drawing scenarios, it considerably aids in overcoming data scarcity. Thereby, it facilitates the validation and comparison of new geometry-generalizing ML methodologies in this domain. By providing this benchmark dataset, we enhance the comparability and validation of emerging methods for ML advancements in sheet metal forming.

With the ever increasing process variability in recent technology nodes, path delay fault testing of digital integrated circuits has become a major challenge. A randomly chosen long path often has no robust test and many of the existing non-robust tests are likely invalidated by process variations. To generate path delay fault tests that are more tolerant towards process variations, the delay test generation must evaluate different non-robust tests and only those tests that sensitize the target path with a sufficiently high probability in presence of process variations must be selected. This requires a huge number of probability computations for a large number of target paths and makes the development of very efficient approximation algorithms mandatory for any practical application. In this paper, a novel and efficient probabilistic sensitization analysis is presented which is used to extract a small subcircuit for a given test vector-pair. The probability that a target path is sensitized by the vector-pair is computed efficiently and without significant error by a Monte-Carlo simulation of the subcircuit.

Large process variations in recent technology nodes present a major challenge for the timing analysis of digital integrated circuits. The optimization decisions of a statistical delay test generation method must therefore rely on the probability of detecting a target delay fault with the currently chosen test vector pairs. However, the huge number of probability evaluations in practical applications creates a large computational overhead. To address this issue, this paper presents the first incremental delay fault detection probability computation algorithm in the literature, which is suitable for the inner loop of automatic test pattern generation methods. Compared to Monte Carlo simulations of NXP benchmark circuits, the new method consistently shows a very large speedup and only a small approximation error.

Increasing parameter variations, caused by variations in process, temperature, power supply, and wear-out, have emerged as one of the most important challenges in semiconductor manufacturing and test. As a consequence for gate delay testing, a single test vector pair is no longer sufficient to provide the required low test escape probabilities for a single delay fault. Recently proposed statistical test generation methods are therefore guided by a metric, which defines the probability of detecting a delay fault with a given test set. However, since runtime and accuracy are dominated by the large number of required metric evaluations, more efficient approximation methods are mandatory for any practical application. In this work, a new statistical dynamic timing analysis algorithm is introduced to tackle this problem. The associated approximation error is very small and predominantly caused by the impact of delay variations on path sensitization and hazards. The experimental results show a large speedup compared to classical Monte Carlo simulations.

In this paper, we propose a new optimization approach for the simultaneous computation of optical flow and edge detection therein. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the optical flow problem as a multidimensional control problem. The optimal control problem is solved by discretization methods and large-scale optimization techniques. The edge detector can be immediately built from the control variables. We provide three series of numerical examples. The first shows that the mere presence of a gradient restriction has a regularizing effect, while the second demonstrates how to balance the regularizing effects of a term within the objective and the control restriction. The third series of numerical results is concerned with the direct evaluation of a TV-regularization term by introduction of control variables with sign restrictions.

We present a new technique for the visualization and analysis of the results from Monte Carlo simulations based on /spl alpha/-complexes and /spl alpha/-shapes. The specific application presented is the analysis of the quantum-mechanical behavior of hydrogen molecules and helium atoms on a surface at very low temperatures. The technique is an improvement over existing techniques in two respects. First, the approach allows one to visualize the points on a random walk at varying levels of detail and interactively select the level of detail that is most appropriate. Second, using /spl alpha/-shapes one can obtain quantitative measures of spatial properties of the system, such as the boundary length and interior area of clusters, that would be difficult to obtain otherwise.>