A topological decoupling of modified nodal analysis including controlled sources

2026-04-22

AI Summary

This work addresses the challenge of efficiently decoupling Modified Nodal Analysis (MNA) equations containing controlled sources in circuit simulation. We propose a constructive graph-theoretic algorithm that, for the first time, achieves topological decoupling of such systems, transforming them into structure-preserving semi-explicit differential-algebraic equations (DAEs) of index 1. The method rigorously maintains the system’s sparsity and positive definiteness, making it well-suited for applications including initial condition generation, model order reduction, and scientific machine learning. Validation on representative circuits with controlled sources demonstrates significant improvements in simulation efficiency. Furthermore, we release the first open-source implementation of a general-purpose decoupling algorithm, establishing a new paradigm for large-scale circuit simulation.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling.

Problem

• modified nodal analysis
• controlled sources
• topological decoupling
• differential-algebraic equations
• circuit simulation

Innovation

• topological decoupling
• modified nodal analysis
• controlled sources
• differential-algebraic equations
• graph-based algorithm