Constitutive modeling of heterogeneous materials by interpretable neural networks: A review

Antonio Bilotta; Emilio Turco; Antonio Bilotta; Emilio Turco

doi:10.3934/nhm.2025012

Networks and Heterogeneous Media

2025, Volume 20, Issue 1: 232-253. doi: 10.3934/nhm.2025012

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Constitutive modeling of heterogeneous materials by interpretable neural networks: A review

Antonio Bilotta ^{1
,
,},
Emilio Turco ²

1.
Department of Informatics, Modelling, Electronics and System Engineering (DIMES), University of Calabria, Via P. Bucci, Cubo 42/C, Rende (CS) 87036, Italy
2.
Department of Architecture, Design and Urban Planning (DADU), University of Sassari, Palazzo del Pou Salit, Piazza Duomo 6, Alghero (SS) 07041, Italy

Received: 18 November 2024 Revised: 27 February 2025 Accepted: 12 March 2025 Published: 24 March 2025

Is it possible to interpret the modeling decisions made by a neural network trained to simulate the constitutive behavior of simple or complex materials? The problem of the interpretability of a neural network is a crucial aspect that has been studied since the first appearance of this type of modeling tool and it is certainly not specific to applications related to constitutive modeling of heterogeneous materials. All areas of application, such as computer vision, biomedicine, and speech, suffer from this fuzziness, and for this reason, neural networks are often referred to as "black-box models". The present work highlighted the efforts dedicated to this aspect in the constitutive modeling of the behavior of path independent materials, reviewing both more standard neural networks and those adopting, more or less strongly, the specific point of view of interpretability.
- constitutive modeling,
- hyperelasticity,
- data-driven,
- machine learning,
- artificial neural networks
Citation: Antonio Bilotta, Emilio Turco. Constitutive modeling of heterogeneous materials by interpretable neural networks: A review[J]. Networks and Heterogeneous Media, 2025, 20(1): 232-253. doi: 10.3934/nhm.2025012

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Abstract

Is it possible to interpret the modeling decisions made by a neural network trained to simulate the constitutive behavior of simple or complex materials? The problem of the interpretability of a neural network is a crucial aspect that has been studied since the first appearance of this type of modeling tool and it is certainly not specific to applications related to constitutive modeling of heterogeneous materials. All areas of application, such as computer vision, biomedicine, and speech, suffer from this fuzziness, and for this reason, neural networks are often referred to as "black-box models". The present work highlighted the efforts dedicated to this aspect in the constitutive modeling of the behavior of path independent materials, reviewing both more standard neural networks and those adopting, more or less strongly, the specific point of view of interpretability.

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