Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Index-aware learning of circuits

Idoia Cortes Garcia, Peter Förster, Lennart Jansen, Wil Schilders, Sebastian Schöps

TL;DR

This work tackles surrogate modeling for electrical circuits by exploiting MNA-derived DAEs through the dissection index to decouple the system into an ODE in differential variables and a set of purely algebraic equations. By learning only the differential variables and reconstructing the algebraic ones from the decoupled system, the approach guarantees algebraic constraints up to solver accuracy and reduces the learning burden. The method is demonstrated for index-one and index-two DAEs via diode-oscillator and rectifier circuits, using Gaussian processes with a sequential variance-based sampling strategy, achieving accurate reconstructions and substantial reduction in the number of learned variables. The framework is architecture- and method-agnostic with respect to the learning component and offers practical benefits for design optimization and uncertainty quantification, with clear paths for extension to controlled sources and electrothermal DAEs.

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.

Index-aware learning of circuits

TL;DR

This work tackles surrogate modeling for electrical circuits by exploiting MNA-derived DAEs through the dissection index to decouple the system into an ODE in differential variables and a set of purely algebraic equations. By learning only the differential variables and reconstructing the algebraic ones from the decoupled system, the approach guarantees algebraic constraints up to solver accuracy and reduces the learning burden. The method is demonstrated for index-one and index-two DAEs via diode-oscillator and rectifier circuits, using Gaussian processes with a sequential variance-based sampling strategy, achieving accurate reconstructions and substantial reduction in the number of learned variables. The framework is architecture- and method-agnostic with respect to the learning component and offers practical benefits for design optimization and uncertainty quantification, with clear paths for extension to controlled sources and electrothermal DAEs.

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.
Paper Structure (22 sections, 1 theorem, 51 equations, 16 figures)

This paper contains 22 sections, 1 theorem, 51 equations, 16 figures.

Table of Contents

  1. Introduction
  2. MNA and DAEs
  3. Index concepts
  4. Example
  5. Index of MNA
  6. Dissection index
  7. Index one case
  8. Index two case
  9. First example circuit
  10. Second example circuit
  11. Index-aware learning
  12. Index one case
  13. Index two case
  14. Example circuits
  15. Numerical examples
  16. ...and 7 more sections

Key Result

theorem 1

Assuming the matrix-valued functions $\mathbf{G} ( \mathbf{A}_\mathrm{R}^{{\!\top}} \boldsymbol{\varphi} )$, $\mathbf{L}(\mathbf{i}_\mathrm{L})$, $\mathbf{C} ( \mathbf{A}_\mathrm{C}^{{\!\top}} \boldsymbol{\varphi} )$ from eq:md_dfj positive definite:

Figures (16)

  • Figure 1: Small example circuit for illustrating the perturbation index.
  • Figure 2: First example circuit: simple diode oscillator.
  • Figure 3: Second example circuit: simple diode oscillator with current instead of voltage source.
  • Figure 4: Schematic workflow of index-aware learning.
  • Figure 5: Solution of the first example circuit for $L = 1.7mH$ and $C = 220nF$.
  • ...and 11 more figures

Theorems & Definitions (6)

  • definition 1
  • theorem 1
  • definition 2
  • definition 3
  • remark 1
  • remark 2