# Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework

arXiv: https://arxiv.org/abs/2404.17583 · HTML: https://mlsanity.com/paper/2404.17583/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 5 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)](https://mlsanity.com/paper/2108.13137/) (2021)
- [A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity](https://mlsanity.com/paper/2204.12088/) (2022)
- [On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning](https://mlsanity.com/paper/2007.07749/) (2020)
- [Physically recurrent neural networks for path-dependent heterogeneous materials: embedding constitutive models in a data-driven surrogate](https://mlsanity.com/paper/2209.07320/) (2022)
- [Recurrent Neural Networks (RNNs) with dimensionality reduction and break down in computational mechanics; application to multi-scale localization step](https://mlsanity.com/paper/2112.12842/) (2021)
- [Symmetry-enforcing neural networks with applications to constitutive modeling](https://mlsanity.com/paper/2312.13511/) (2023)
- [A Neural Network Transformer Model for Composite Microstructure Homogenization](https://mlsanity.com/paper/2304.07877/) (2023)
- [NN-EVP: A physics informed neural network-based elasto-viscoplastic framework for predictions of grain size-aware flow response under large deformations](https://mlsanity.com/paper/2307.04301/) (2023)
- [Recurrent neural networks and transfer learning for elasto-plasticity in woven composites](https://mlsanity.com/paper/2311.13434/) (2023)
- [Explainable artificial intelligence for mechanics: physics-informing neural networks for constitutive models](https://mlsanity.com/paper/2104.10683/) (2021)

## Built on by (most cited first, 3 of 3)

- [One-Step Flow Matching for Generative Modeling of Path-Dependent Physical Fields](https://mlsanity.com/paper/2606.22752/) (2026)
- [Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites](https://mlsanity.com/paper/2607.13688/) (2026)
- [On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regime](https://mlsanity.com/paper/2610.04067/) (2026)

## Abstract (arXiv)

In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding them in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained.