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arXiv · 2510.09317

Residual-Informed Learning of Solutions to Algebraic Loops

Felix Brandt·Andreas Heuermann·Philip Hannebohm·Bernhard Bachmann
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Abstract

This paper presents a residual-informed machine learning approach for replacing algebraic loops in equation-based Modelica models with neural network surrogates. A feedforward neural network is trained using the residual (error) of the algebraic loop directly in its loss function, eliminating the need for a supervised dataset. This training strategy also resolves the issue of ambiguous solutions, allowing the surrogate to converge to a consistent solution rather than averaging multiple valid ones. Applied to the large-scale IEEE 14-Bus system, our method achieves a 60% reduction in simulation time compared to conventional simulations, while maintaining the same level of accuracy through error control mechanisms.

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Felix Brandt, Andreas Heuermann, Philip Hannebohm, Bernhard Bachmann. 2025-10-10. Residual-Informed Learning of Solutions to Algebraic Loops. https://arxiv.org/abs/2510.09317

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