Physics-informed neural networks for predicting high-strain-rate energy absorption in additively manufactured lattice materials

Abstract

Predicting the dynamic response of additively manufactured lattice structures remains challenging due to data scarcity and the complex coupling between geometry, strain-rate, and material behavior. This study presents a Physics-Informed Neural Network (PINN) framework for modeling high-strain-rate energy absorption in laser powder bed fusion (LPBF)-fabricated A286 steel lattices. The proposed model integrates the linear-elastic constitutive law \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upsigma ={\text{E}}_{\text{eff}}\upvarepsilon$$\end{document} within the loss function to couple experimental data with physics-based regularization. The effective modulus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{\text{eff}}$$\end{document} was derived from CAD-based relative densities using the Gibson-Ashby scaling relation, ensuring topology-specific stiffness representation for honeycomb, BCC, and gyroid lattices. The curated dataset comprised 108 Split Hopkinson Pressure Bar (SHPB) tests spanning 2-6 bar impact pressures. The PINN achieved R2 = 0.988, RMSE = 1.28 J, and MAE = 1.05 J, outperforming the data-only neural network (Delta R2 = + 0.034) and classical machine-learning baselines. SHAP analysis confirmed that impact pressure and lattice topology govern the predictive response, consistent with mechanical intuition. The embedded physics constraint enhanced generalization, mitigated overfitting under limited data, and improved interpretability of learned stress-strain-energy correlations. The framework establishes a pathway for integrating first-principles knowledge with deep learning to predict high-rate mechanical behavior in architected materials and can be extended toward cross-topology and cross-alloy generalization through transfer-learning and simulation-augmented training.