{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:59:42Z","timestamp":1778597982331,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T00:00:00Z","timestamp":1641772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1852215"],"award-info":[{"award-number":["CCF-1852215"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Physics-informed machine learning is emerging through vast methodologies and in various applications. This paper discovers physics-based custom loss functions as an implementable solution to additive manufacturing (AM). Specifically, laser metal deposition (LMD) is an AM process where a laser beam melts deposited powder, and the dissolved particles fuse to produce metal components. Porosity, or small cavities that form in this printed structure, is generally considered one of the most destructive defects in metal AM. Traditionally, computer tomography scans measure porosity. While this is useful for understanding the nature of pore formation and its characteristics, purely physics-driven models lack real-time prediction ability. Meanwhile, a purely deep learning approach to porosity prediction leaves valuable physics knowledge behind. In this paper, a hybrid model that uses both empirical and simulated LMD data is created to show how various physics-informed loss functions impact the accuracy, precision, and recall of a baseline deep learning model for porosity prediction. In particular, some versions of the physics-informed model can improve the precision of the baseline deep learning-only model (albeit at the expense of overall accuracy).<\/jats:p>","DOI":"10.3390\/s22020494","type":"journal-article","created":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T22:03:13Z","timestamp":1641852193000},"page":"494","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["A Physics-Informed Convolutional Neural Network with Custom Loss Functions for Porosity Prediction in Laser Metal Deposition"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7565-3052","authenticated-orcid":false,"given":"Erin","family":"McGowan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Rutgers University, New Brunswick, Piscataway, NJ 08854, USA"}]},{"given":"Vidita","family":"Gawade","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Rutgers University, New Brunswick, Piscataway, NJ 08854, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8433-6326","authenticated-orcid":false,"given":"Weihong (Grace)","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Rutgers University, New Brunswick, Piscataway, NJ 08854, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.matdes.2015.06.135","article-title":"Laser metal deposition of functionally graded Ti6Al4V\/TiC","volume":"84","author":"Mahamood","year":"2015","journal-title":"Mater. Des."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1002\/latj.201090029","article-title":"Laser Additive Manufacturing: Laser Metal Deposition (LMD) and Selective Laser Melting (SLM) in Turbo-Engine Applications","volume":"7","author":"Gasser","year":"2010","journal-title":"Laser Tech. J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Brandt, M. (2017). 13-Aerospace applications of laser additive manufacturing. Laser Additive Manufacturing, Woodhead Publishing.","DOI":"10.1016\/B978-0-08-100433-3.02001-7"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.jallcom.2019.04.255","article-title":"Additive manufacturing of Ti\u20136Al\u20134V parts through laser metal deposition (LMD): Process, microstructure, and mechanical properties","volume":"804","author":"Azarniya","year":"2019","journal-title":"J. Alloys Compd."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Oskolkov, A., Bezukladnikov, I., and Trushnikov, D. (2021). Indirect Temperature Measurement in High Frequency Heating Systems. Sensors, 21.","DOI":"10.3390\/s21072561"},{"key":"ref_6","first-page":"443","article-title":"Dual Process Monitoring of Metal-based Additive Manufacturing using Tensor Decomposition of Thermal Image Streams","volume":"23","author":"Khanzadeh","year":"2018","journal-title":"Addit. Manuf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1007\/s11837-015-1767-z","article-title":"Understanding the Microstructure Formation of Ti-6Al-4V During Direct Laser Deposition via In-Situ Thermal Monitoring","volume":"68","author":"Marshall","year":"2016","journal-title":"JOM"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1080\/24725854.2017.1417656","article-title":"In-Situ Monitoring of Melt Pool Images for Porosity Prediction in Directed Energy Deposition Processes","volume":"51","author":"Khanzadeh","year":"2019","journal-title":"IISE Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/24725854.2018.1478169","article-title":"Layer-Wise Spatial Modeling of Porosity in Additive Manufacturing","volume":"51","author":"Liu","year":"2019","journal-title":"IISE Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF02667333","article-title":"A New Finite Element Model for Welding Heat Sources","volume":"15","author":"Goldak","year":"1984","journal-title":"Metall. Trans. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1080\/02670836.2018.1489939","article-title":"Strategy of computational predictions for mechanical behaviour of additively manufactured materials","volume":"34","author":"Zinovieva","year":"2018","journal-title":"Mater. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"052006","DOI":"10.2351\/1.4817788","article-title":"Heat transfer and fluid flow in additive manufacturing","volume":"25","author":"Raghavan","year":"2013","journal-title":"J. Laser Appl."},{"key":"ref_13","first-page":"548","article-title":"Melt pool temperature and cooling rates in laser powder bed fusion","volume":"22","author":"Hooper","year":"2018","journal-title":"Addit. Manuf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1146\/annurev.matsci.32.101901.155803","article-title":"Phase-field simulation of solidification","volume":"32","author":"Boettinger","year":"2002","journal-title":"Annu. Rev. Mater. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0956-7151(93)90065-Z","article-title":"Probabilistic modelling of microstructure formation in solidification processes","volume":"41","author":"Rappaz","year":"1993","journal-title":"Acta Metall. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107672","DOI":"10.1016\/j.matdes.2019.107672","article-title":"A cellular automaton finite volume method for microstructure evolution during additive manufacturing","volume":"169","author":"Lian","year":"2019","journal-title":"Mater. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"142447","DOI":"10.1016\/j.msea.2021.142447","article-title":"Effects of scanning pattern on the grain structure and elastic properties of additively manufactured 316L austenitic stainless steel","volume":"832","author":"Zinovieva","year":"2021","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.matdes.2016.01.099","article-title":"Review of in-situ process monitoring and in-situ metrology for metal additive manufacturing","volume":"95","author":"Everton","year":"2016","journal-title":"Mater. Des."},{"key":"ref_19","first-page":"135","article-title":"Assessing the capability of in-situ nondestructive analysis during layer based additive manufacture","volume":"13","author":"Hirsch","year":"2017","journal-title":"Addit. Manuf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"015029","DOI":"10.1088\/2051-672X\/abedf9","article-title":"Material ratio curve of 3D surface topography of additively manufactured parts: An attempt to characterise open surface pores","volume":"9","author":"Lou","year":"2021","journal-title":"Surf. Topogr. Metrol. Prop."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wojnowski, W., Kalinowska, K., G\u0119bicki, J., and Zabiega\u0142a, B. (2020). Monitoring the BTEX Volatiles during 3D Printing with Acrylonitrile Butadiene Styrene (ABS) Using Electronic Nose and Proton Transfer Reaction Mass Spectrometry. Sensors, 20.","DOI":"10.3390\/s20195531"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"041011","DOI":"10.1115\/1.4048957","article-title":"Deep Learning-Based Data Fusion Method for In Situ Porosity Detection in Laser-Based Additive Manufacturing","volume":"143","author":"Tian","year":"2021","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gawade, V., Singh, V., and Guo, W. (2021). Leveraging Simulated and Empirical Data-Driven Insight to Supervised-Learning for Porosity Prediction in Laser Metal Deposition. J. Manuf. Syst.","DOI":"10.1016\/j.jmsy.2021.07.013"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.jmsy.2018.04.001","article-title":"Porosity prediction: Supervised-learning of thermal history for direct laser deposition","volume":"47","author":"Khanzadeh","year":"2018","journal-title":"J. Manuf. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Yang, Z., Lu, Y., Yeung, H., and Krishnamurty, S. (2019, January 22\u201326). Investigation of Deep Learning for Real-Time Melt Pool Classification in Additive Manufacturing. Proceedings of the 2019 IEEE 15th International Conference on Automation Science and Engineering (CASE), Vancouver, BC, Canada.","DOI":"10.1109\/COASE.2019.8843291"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cirp.2020.04.049","article-title":"A Physics-Driven Deep Learning Model for Process-Porosity Causal Relationship and Porosity Prediction with Interpretability in Laser Metal Deposition","volume":"69","author":"Guo","year":"2020","journal-title":"CIRP Ann.-Manuf. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-informed machine learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"ref_28","unstructured":"Willard, J., Jia, X., Xu, S., Steinbach, M., and Kumar, V. (2020). Integrating Physics-Based Modeling with Machine Learning: A Survey. arXiv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4695","DOI":"10.1007\/s11837-020-04438-4","article-title":"Physics-Informed and Hybrid Machine Learning in Additive Manufacturing: Application to Fused Filament Fabrication","volume":"72","author":"Kapusuzoglu","year":"2020","journal-title":"JOM"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1007\/s00170-021-06640-3","article-title":"A Physics-Informed Machine Learning Model for Porosity Analysis in Laser Powder Bed Fusion Additive Manufacturing","volume":"113","author":"Liu","year":"2021","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_31","unstructured":"Karpatne, A., Watkins, W., Read, J., and Kumar, V. (2018). Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s00466-020-01952-9","article-title":"Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks","volume":"67","author":"Zhu","year":"2021","journal-title":"Comput. Mech."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Barton, S., Alakkari, S., O\u2019Dwyer, K., Ward, T., and Hennelly, B. (2021). Convolution Network with Custom Loss Function for the Denoising of Low SNR Raman Spectra. Sensors, 21.","DOI":"10.3390\/s21144623"},{"key":"ref_34","first-page":"1","article-title":"Classification vs regression in overparameterized regimes: Does the loss function matter?","volume":"22","author":"Muthukumar","year":"2021","journal-title":"J. Mach. Learn. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/j.dib.2016.02.084","article-title":"Data indicating temperature response of Ti\u20136Al\u20134V thin-walled structure during its additive manufacture via Laser Engineered Net Shaping","volume":"7","author":"Marshall","year":"2016","journal-title":"Data Brief"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.promfg.2015.09.012","article-title":"Thermal Modeling of Laser Based Additive Manufacturing Processes within Common Materials","volume":"1","author":"Romano","year":"2015","journal-title":"Procedia Manuf."},{"key":"ref_37","unstructured":"Simonyan, K., and Zisserman, A. (2015). Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/494\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:01:51Z","timestamp":1760364111000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,10]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["s22020494"],"URL":"https:\/\/doi.org\/10.3390\/s22020494","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,10]]}}}