# Residual-Informed Learning of Solutions to Algebraic Loops

arXiv: https://arxiv.org/abs/2510.09317 · HTML: https://mlsanity.com/paper/2510.09317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [Don't Unroll Adjoint: Differentiating SSA-Form Programs](https://mlsanity.com/paper/1810.07951/) (2018)

## Abstract (arXiv)

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.