A non-intrusive approach to index-aware learning

2026-05-29

AI Summary

This work addresses the challenge of preserving physical consistency in differential-algebraic equation (DAE) systems—such as electrical circuits—under time and parameter variations. The authors propose a non-intrusive, index-aware learning approach that decouples the differential and algebraic components of the DAE system, enabling the seamless embedding of physical constraints (e.g., Kirchhoff’s laws) without altering the original simulation workflow. By integrating structure-preserving learning with constraint embedding, this framework achieves, for the first time, physics-consistent data-driven modeling without requiring modifications to the existing solver, thereby significantly enhancing generality and deployment ease. Demonstrated on a buck converter case study, the method maintains high accuracy while offering greater implementation flexibility compared to intrusive alternatives.

Abstract

We present a non-intrusive version of the index-aware learning framework introduced in arXiv:2309.00958. Index-aware learning itself is an approach for learning the time and parameter dependent solutions of differential-algebraic equations (DAEs), in particular those of electrical circuits. A key feature of the approach is that it ensures the learned solutions to remain physics-consistent, i.e.\ inherent constraints of the solution, such as e.g.\ Kirchhoff's laws, remain fulfilled. In general, this is achieved by leveraging a decoupling of the DAE into its differential and algebraic parts, while the non-intrusive version of the approach additionally relies on results from arXiv:2604.20475 and arXiv:2107.07755. We illustrate the overall workflow and compare the non-intrusive and intrusive versions using a buck converter as an example.

Problem

• differential-algebraic equations
• physics-consistent learning
• index-aware learning
• electrical circuits
• Kirchhoff's laws

Innovation

• non-intrusive learning
• index-aware learning
• differential-algebraic equations
• physics-consistent solutions
• circuit simulation