{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:30:33Z","timestamp":1787027433249,"version":"build-2736575974"},"reference-count":45,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009391","name":"Kafkas University","doi-asserted-by":"publisher","award":["2023-FM-40"],"award-info":[{"award-number":["2023-FM-40"]}],"id":[{"id":"10.13039\/501100009391","id-type":"DOI","asserted-by":"publisher"}]},{"award":["2023-FM-40"],"award-info":[{"award-number":["2023-FM-40"]}],"id":[{"id":"https:\/\/ror.org\/04v302n28","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This study presents a methodology for predicting the geometric features of single tracks of 316L stainless steel produced by Powder-Bed Arc Additive Manufacturing (PBAAM) from four independent process parameters using a multi-modal Physics-Informed Neural Network (PINN). PBAAM shares the same powder-deposition and layering scheme as Laser Powder Bed Fusion (LPBF) but uses a low-current micro-TIG arc rather than a laser as the heat source. A multi-task PINN architecture was developed that simultaneously predicts five geometric features measured from two imaging modalities (top-view and side-view arc), namely the arc core diameter (Dq), the arc cone angle (\u03b1c), the heat-affected zone width (wHAZ), the track core width (dcore) and the areal equivalent track width (wiz), from four input parameters (arc current, traverse speed, work angle and working distance). The model was assessed on a full-factorial training matrix of 36 experiments and on four pure speed extrapolation experiments above the training range. A composite quality score filter classified 23 of the training experiments as stable and 13 as unstable. On the pure validation set, the mean absolute percentage error (MAPE) was 4.25% (95% confidence interval 0.91\u20138.49) for the arc core diameter, 6.29% (5.07\u20137.59) for the arc cone angle, 8.06% (6.08\u20139.82) for the heat-affected zone width, and 17.02% (10.77\u201321.62) for the track core width. Classical regression baselines attain comparable aggregate errors on this narrowly distributed validation set; the distinguishing property of the proposed model is the joint, physically ordered prediction of all five outputs. The Ayrton voltage sub-module of the model converged to U(I) = 11.33 + 97.13\/I without any direct voltage measurement, purely through the physics loss term; this function is consistent with the order of magnitude expected from the physics of low-current TIG arcs. The results indicate that physics-informed learning can be applied to the PBAAM process parameter space under small-sample conditions. This capability is demonstrated for 316L stainless steel, for the micro-TIG electrode configuration and the process window investigated here, for single tracks rather than multi-layer builds, and against a validation set of four experiments varying in a single direction.<\/jats:p>","DOI":"10.3390\/ma19163454","type":"journal-article","created":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T15:48:36Z","timestamp":1786722516000},"page":"3454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Modal Physics-Informed Neural Network for Single-Track Geometry Prediction in Powder-Bed Arc Additive Manufacturing of 316L Stainless Steel"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4932-9654","authenticated-orcid":false,"given":"Arif","family":"Balc\u0131","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering and Architecture, Kafkas University, Kars 36100, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.actamat.2016.02.014","article-title":"Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones","volume":"108","author":"Khairallah","year":"2016","journal-title":"Acta Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"166245","DOI":"10.1016\/j.jallcom.2022.166245","article-title":"Powder Plasma Arc Additive Manufacturing of CoCrFeNiWx High-Entropy Alloys: Microstructure Evolution and Mechanical Properties","volume":"922","author":"Shen","year":"2022","journal-title":"J. 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