Residual-Informed Learning of Solutions to Algebraic Loops

2025/10/10 by Felix Brandt, Andreas Heuermann, Brandt, Felix +5
Computer Science · Engineering · Physics and Astronomy · #37M05 #65H10 #FOS: Computer and information sciences #FOS: Mathematics #G.1.5 #I.2.6 #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Modeling and Simulation Systems #Numerical Analysis (math.NA) #Power System Optimization and Stability

paper · pdf · doi:10.48550/arxiv.2510.09317

openalex publication_date 2025/10/10 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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• Don't Unroll Adjoint: Differentiating SSA-Form Programs

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