TY - JOUR

T1 - Index-aware learning of circuits

AU - Cortes Garcia, Idoia

AU - Förster, Peter

AU - Jansen, Lennart

AU - Schilders, Wil H.A.

AU - Schöps, Sebastian

PY - 2024/4/8

Y1 - 2024/4/8

N2 - 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, for example, 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.

AB - 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, for example, 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.

KW - differential-algebraic equations

KW - dissection index

KW - electrical circuits

KW - machine learning

KW - modified nodal analysis

UR - http://www.scopus.com/inward/record.url?scp=85190249183&partnerID=8YFLogxK

U2 - 10.1002/cta.4024

DO - 10.1002/cta.4024

M3 - Article

SN - 0098-9886

VL - XX

JO - International Journal of Circuit Theory and Applications

JF - International Journal of Circuit Theory and Applications

IS - X

ER -