Data Driven Process Maps for Foam Additive Manufacturing: Accuracy and Interpretability Across Six Models

Data Driven Process Maps for Foam Additive Manufacturing: Accuracy and Interpretability Across Six Models | 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 Research Article Data Driven Process Maps for Foam Additive Manufacturing: Accuracy and Interpretability Across Six Models Andrea Lorenzo Henri Sergio Detry, Daniele Vanerio, Antonino Squillace This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8244263/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Foam Additive Manufacturing (FAM) couples gas-assisted foaming with material extrusion to produce lightweight PLA components, yet the combined influence of solubilization and extrusion variables remains poorly quantified. We analyze 528 experiments on PLA foamed with CO₂ and model strand density (ρ) as a function of six controllable parameters (Pₐ, tₐ, t_d, Tₑ, Sₑ, Dₙ). We compare six regressors (polynomial, PCA + polynomial, SVR-RBF, Random Forest, RF-distilled polynomial surrogate, and MLP) using an identical 80/20 held-out test partition and a standardized map-generation protocol. The Bayesian-regularized MLP attains the highest nominal accuracy(MAE = 0.0925 g/cm³, RMSE = 0.1216 g/cm³, R² = 0.832),while the Random Forest provides the most reliable non-neural baseline(R² = 0.41, RMSE = 0.141 g/cm³). To reconcile accuracy and interpretability, we distill the Random Forest into a degree-2 polynomial surrogate that yields a closed-form, differentiable mapping with competitive error and enables analytic process maps and gradient-based optimization. The resulting maps quantify interactions among Tₑ and Sₑ at fixed (Pₐ, tₐ, t_d), revealing physically consistent trends (density decreases with increasing Sₑ; mild increase with Tₑ). This study delivers a hybrid framework—ensemble accuracy plus polynomial transparency—for predictive design and multivariable control in FAM, and establishes reproducible benchmarks and artifacts (code, splits, figures) to support deployment in digital twins and closed-loop process planning. Foam additive manufacturing Physical foaming PLA CO2 solubilization Process maps Machine learning Random Forest Polynomial surrogate Bayesian regularization Multi-layer perceptron Digital twin Closed-loop process control Full Text Additional Declarations No competing interests reported. Supplementary Files SuppMatAnonymus.tex Cite Share Download PDF Status: Posted Version 1 posted 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-8244263","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":554881678,"identity":"a24dd509-5816-4606-b969-f7747f7c6144","order_by":0,"name":"Andrea Lorenzo Henri Sergio 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We analyze 528 experiments on PLA foamed with CO₂ and model strand density (ρ) as a function of six controllable parameters (Pₐ, tₐ, t_d, Tₑ, Sₑ, Dₙ).\nWe compare six regressors (polynomial, PCA + polynomial, SVR-RBF, Random Forest, RF-distilled polynomial surrogate, and MLP) using an identical 80/20 held-out test partition and a standardized map-generation protocol.\nThe Bayesian-regularized MLP attains the highest nominal accuracy(MAE = 0.0925 g/cm³, RMSE = 0.1216 g/cm³, R² = 0.832),while the Random Forest provides the most reliable non-neural baseline(R² = 0.41, RMSE = 0.141 g/cm³).\nTo reconcile accuracy and interpretability, we distill the Random Forest into a degree-2 polynomial surrogate that yields a closed-form, differentiable mapping with competitive error and enables analytic process maps and gradient-based optimization.\nThe resulting maps quantify interactions among Tₑ and Sₑ at fixed (Pₐ, tₐ, t_d), revealing physically consistent trends (density decreases with increasing Sₑ; mild increase with Tₑ). 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