Physics Informed Activation Functions and Loss Functions for Signal Reconstruction and Digital Twinning

Physics Informed Activation Functions and Loss Functions for Signal Reconstruction and Digital Twinning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Physics Informed Activation Functions and Loss Functions for Signal Reconstruction and Digital Twinning Brent Cook, Adryel Gainza, Bryan Portocarrero, Mubarak Mujawar, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8140679/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 15 You are reading this latest preprint version Abstract A coupled two-body mass Lagrangian is used to model a magnetic rail nScrypt printer extruder with a sensor attached to the side for signal reconstruction and digital twinning. The equations of motion (EQM) derived from the Lagrangian are then used to improve the accelerometer signal by incorporating them as activation functions in the layers of the neural network, then using the damping constant and frequency matrix as learnable parameters. This is compared to a modular neural network that uses the EQM as the loss residuals for backward propagation and the physical constants as neural nets, both methods were found to give a root-mean square error (RMSE) of 14 mm to 0.75 mm from the original position signal respectively. The physics informed neural network (PINN) activation layer produced a better detailed fit, while the PINN loss function produced a better average line. The two methods are then combined to achieve a final result with an RMSE of 1.52 mm to 16.94 mm with better detail but higher variability. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Neural Networks Physics-Informed Neural Networks Activation Function Loss Function Printing Digital Twinning Full Text Additional Declarations No competing interests reported. Supplementary Files 251109SupportingInformation.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Mar, 2026 Reviewers agreed at journal 28 Mar, 2026 Reviews received at journal 26 Mar, 2026 Reviewers agreed at journal 24 Mar, 2026 Reviews received at journal 05 Mar, 2026 Reviewers agreed at journal 05 Mar, 2026 Reviewers agreed at journal 04 Jan, 2026 Reviews received at journal 01 Jan, 2026 Reviewers agreed at journal 30 Dec, 2025 Reviewers agreed at journal 30 Dec, 2025 Reviewers invited by journal 19 Dec, 2025 Editor invited by journal 26 Nov, 2025 Editor assigned by journal 20 Nov, 2025 Submission checks completed at journal 20 Nov, 2025 First submitted to journal 17 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8140679","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":562865249,"identity":"212cae35-3b10-4d93-a3f0-7a8f36c5a2d7","order_by":0,"name":"Brent 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