Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify 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 use the recently introduced dissection index that can decouple a given system of DAEs into ordinary differential equations, only depending on differential variables, and purely algebraic equations, that describe the relations between differential and algebraic variables. The idea is to then 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, and it may also reduce the learning effort as only the differential variables need to be learned.

翻译：电路存在于多种技术中，其设计是计算机辅助工程的重要组成部分。影响最终设计的参数数量不断增加，因此需要新方法来量化其影响。机器学习在此方面可能发挥关键作用，然而当前方法往往未能充分利用系统已有的知识。就电路而言，通过改进节点分析对其进行的描述已得到充分理解。这种特定表述会导致微分代数方程组（DAEs），这些方程组带来诸多特性，例如解需满足的隐式约束。我们采用最近引入的分割索引，该索引可将给定的DAE系统解耦为仅依赖于微分变量的常微分方程，以及描述微分变量与代数变量之间关系的纯代数方程。其核心思想是仅学习微分变量，并利用解耦关系重建代数变量。该方法可保证代数约束满足至非线性系统求解器的精度，同时由于只需学习微分变量，还可能降低学习成本。