Electrical circuits are present in a variety of technologies, making their
design an important part of computer aided engineering. The growing number of
tunable parameters that affect the final design leads to a need for new
approaches of quantifying their impact. Machine learning may play a key role in
this regard, however current approaches often make suboptimal use of existing
knowledge about the system at hand. In terms of circuits, their description via
modified nodal analysis is well-understood. This particular formulation leads
to systems of differential-algebraic equations (DAEs) which bring with them a
number of peculiarities, e.g. hidden constraints that the solution needs to
fulfill. We aim to use the recently introduced dissection concept for DAEs that
can decouple a given system into ordinary differential equations, only
depending on differential variables, and purely algebraic equations that
describe the relations between differential and algebraic variables. The idea
then is to only learn the differential variables and reconstruct the algebraic
ones using the relations from the decoupling. This approach guarantees that the
algebraic constraints are fulfilled up to the accuracy of the nonlinear system
solver, which represents the main benefit highlighted in this article.

电路的设计是计算机辅助工程中的重要部分，而有关可调参数对最终设计的影响的量化需要新的方法。本文介绍了一种基于机器学习和改进的节点分析的方法，通过解耦系统方程，只学习微分变量并使用解耦关系重构代数变量，从而保证了代数约束的准确性。

电路的索引感知学习

Index-aware learning of circuits

In this work, we establish a method for abstracting information from Computer
Aided Engineering (CAE) into graphs. Such graph representations of CAE data can
improve design guidelines and support recommendation systems by enabling the
comparison of simulations, highlighting unexplored experimental designs, and
correlating different designs. We focus on the load-path in crashworthiness
analysis, a complex sub-discipline in vehicle design. The load-path is the
sequence of parts that absorb most of the energy caused by the impact. To
detect the load-path, we generate a directed weighted graph from the CAE data.
The vertices represent the vehicle's parts, and the edges are an abstraction of
the connectivity of the parts. The edge direction follows the temporal
occurrence of the collision, where the edge weights reflect aspects of the
energy absorption. We introduce and assess three methods for graph extraction
and an additional method for further updating each graph with the sequences of
absorption. Based on longest-path calculations, we introduce an automated
detection of the load-path, which we analyse for the different graph extraction
methods and weights. Finally, we show how our method for the detection of
load-paths helps in the classification and labelling of CAE simulations.

本文建立了一种从计算机辅助工程（CAE）中抽象出图形信息的方法，特别是关注了复杂的车辆设计，提出了利用图形表示 CAE 数据的概念，并引入了自动检测载荷路径的方法，有助于 CAE 模拟结果的分类和标记。