{"citation":{"ama":"Brandt F, Heuermann A, Hannebohm P, Bachmann B. Residual-Informed Learning of Solutions to Algebraic Loops. <i>arXiv:251009317</i>. 2025.","mla":"Brandt, Felix, et al. “Residual-Informed Learning of Solutions to Algebraic Loops.” <i>ArXiv:2510.09317</i>, 2025.","ieee":"F. Brandt, A. Heuermann, P. Hannebohm, and B. Bachmann, “Residual-Informed Learning of Solutions to Algebraic Loops,” <i>arXiv:2510.09317</i>. 2025.","alphadin":"<span style=\"font-variant:small-caps;\">Brandt, Felix</span> ; <span style=\"font-variant:small-caps;\">Heuermann, Andreas</span> ; <span style=\"font-variant:small-caps;\">Hannebohm, Philip</span> ; <span style=\"font-variant:small-caps;\">Bachmann, Bernhard</span>: Residual-Informed Learning of Solutions to Algebraic Loops. In: <i>arXiv:2510.09317</i> (2025)","apa":"Brandt, F., Heuermann, A., Hannebohm, P., &#38; Bachmann, B. (2025). Residual-Informed Learning of Solutions to Algebraic Loops. <i>ArXiv:2510.09317</i>.","chicago":"Brandt, Felix, Andreas Heuermann, Philip Hannebohm, and Bernhard Bachmann. “Residual-Informed Learning of Solutions to Algebraic Loops.” <i>ArXiv:2510.09317</i>, 2025.","bibtex":"@article{Brandt_Heuermann_Hannebohm_Bachmann_2025, title={Residual-Informed Learning of Solutions to Algebraic Loops}, journal={arXiv:2510.09317}, author={Brandt, Felix and Heuermann, Andreas and Hannebohm, Philip and Bachmann, Bernhard}, year={2025} }","short":"F. Brandt, A. Heuermann, P. Hannebohm, B. Bachmann, ArXiv:2510.09317 (2025)."},"_id":"6448","title":"Residual-Informed Learning of Solutions to Algebraic Loops","abstract":[{"lang":"eng","text":"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."}],"language":[{"iso":"eng"}],"date_created":"2026-01-14T16:09:00Z","oa":"1","user_id":"263827","status":"public","date_updated":"2026-01-15T09:05:48Z","type":"preprint","author":[{"first_name":"Felix","last_name":"Brandt","full_name":"Brandt, Felix"},{"first_name":"Andreas","last_name":"Heuermann","full_name":"Heuermann, Andreas"},{"orcid_put_code_url":"https://api.orcid.org/v2.0/0009-0003-8902-9079/work/202504693","last_name":"Hannebohm","first_name":"Philip","full_name":"Hannebohm, Philip","id":"221456","orcid":"0009-0003-8902-9079"},{"full_name":"Bachmann, Bernhard","id":"33931","orcid":"0000-0002-4339-0438","first_name":"Bernhard","last_name":"Bachmann","orcid_put_code_url":"https://api.orcid.org/v2.0/0000-0002-4339-0438/work/202504694"}],"main_file_link":[{"open_access":"1"}],"year":"2025","publication":"arXiv:2510.09317"}