mlsanityData to 14 Oct 2026

Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables

arXiv 2308.03915 ↗First posted 7 Aug 2023cs.LG physics.comp-phcited by 1

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Abstract (arXiv)

Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, Neural Network methods have arisen as powerful tools to identify very complex and non-linear correlations. In this work, we use the very recently developed concept of Physically Guided Neural Networks with Internal Variables (PGNNIV) to discover constitutive laws using a model-free approach and training solely with measured force-displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen load scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, placing the method in what is known as eXplainable Artificial Intelligence (XAI).

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 36 of its 111 references that are in the map. First posted on arXiv 7 Aug 2023.

Builds on

36 of 111 references.

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24 more
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  1. 2025Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variablescited by 0