Artificial neural network surrogate modeling for explosively formed projectiles using space filling sampling

This study provides a surrogate framework that combines high fidelity Finite Element Method ( FEM ) calculations and Artificial Neural Network ( ANN ) topologies, to efficiently evaluate the multiphysical performance of Explosively Formed Projectiles ( EFP ). The geometric domain was discretized with 64 design samples using a space filling approach. Physically unstable configurations were eliminated, resulting in a refined dataset of 62 samples, demonstrating high data efficiency compared to exhaustive grid-based sampling strategies. The regularized neural network was compared to Response Surface Methodology, Support Vector Regression and Random Forest models using a Repeated K Fold Cross Validation methodology. Mathematical solutions of severe nonlinear mechanical dependencies were obtained by optimization using the Limited memory Broyden Fletcher Goldfarb Shanno ( L-BFGS ) algorithm combined with L 2 regularization. Standard machine learning models overfit the chaotic physical phases such projectile stretching, as demonstrated by rigorous cross validation, while the neural network exhibited superior out-of-sample generalization for kinematic and morphological parameters, and remained highly competitive for terminal ballistic variables. The kinematic velocity was statistically evaluated with a mean determination coefficient of 0.9977 and penetration depth of 0.8091. Live-fire tests validated the framework with relative errors below 6% for velocity and 15% for crater growth. Rather than a standalone inverse-design tool, this framework provides a data-efficient rapid screening methodology for precision-guided munitions, significantly reducing computational costs prior to empirical verification.

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Publication Details

Journal
International Journal of Protective Structures
Published
2026-09-17
DOI
https://doi.org/10.1177/20414196261488970
Primary Topic
High-Velocity Impact and Material Behavior
Type
article
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article

Artificial neural network surrogate modeling for explosively formed projectiles using space filling sampling

Pham Hong Quan, Nguyen Van Tien, Do Van Thom, Tran Dinh Thanh
International Journal of Protective Structures
High-Velocity Impact and Material Behavior
article

Artificial neural network surrogate modeling for explosively formed projectiles using space filling sampling

Pham Hong Quan, Nguyen Van Tien, Do Van Thom, Tran Dinh Thanh
article en

Abstract

This study provides a surrogate framework that combines high fidelity Finite Element Method ( FEM ) calculations and Artificial Neural Network ( ANN ) topologies, to efficiently evaluate the multiphysical performance of Explosively Formed Projectiles ( EFP ). The geometric domain was discretized with 64 design samples using a space filling approach. Physically unstable configurations were eliminated, resulting in a refined dataset of 62 samples, demonstrating high data efficiency compared to exhaustive grid-based sampling strategies. The regularized neural network was compared to Response Surface Methodology, Support Vector Regression and Random Forest models using a Repeated K Fold Cross Validation methodology. Mathematical solutions of severe nonlinear mechanical dependencies were obtained by optimization using the Limited memory Broyden Fletcher Goldfarb Shanno ( L-BFGS ) algorithm combined with L 2 regularization. Standard machine learning models overfit the chaotic physical phases such projectile stretching, as demonstrated by rigorous cross validation, while the neural network exhibited superior out-of-sample generalization for kinematic and morphological parameters, and remained highly competitive for terminal ballistic variables. The kinematic velocity was statistically evaluated with a mean determination coefficient of 0.9977 and penetration depth of 0.8091. Live-fire tests validated the framework with relative errors below 6% for velocity and 15% for crater growth. Rather than a standalone inverse-design tool, this framework provides a data-efficient rapid screening methodology for precision-guided munitions, significantly reducing computational costs prior to empirical verification.

International Journal of Protective Structures
Le Quy Don Technical University (VN), University Of Transport Technology (VN)
Life in Land
Openalex Percentile: Top 24%
High-Velocity Impact and Material Behavior
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