Index-aware learning of circuits

TL;DR

This paper introduces an index-aware learning approach for electrical circuits that leverages the dissection index to decouple DAEs, enabling more efficient and accurate learning of circuit behavior by focusing on differential variables.

Contribution

The paper proposes a novel method that uses the dissection index to decouple DAEs in circuit models, improving learning efficiency and constraint satisfaction.

Findings

Decoupling DAEs simplifies the learning process.

Learning only differential variables reduces complexity.

Constraints are maintained up to solver accuracy.

Abstract

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.