# Data-Driven Dynamic Friction Models based on Recurrent Neural Networks

arXiv: https://arxiv.org/abs/2402.14148 · HTML: https://mlsanity.com/paper/2402.14148/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 71 references that are in the map.
- First posted on arXiv 21 Feb 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning](https://mlsanity.com/paper/1810.10535/) (2018)
- [Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2205.00578/) (2022)
- [Physics-Informed Deep Learning of Rate-and-State Fault Friction](https://mlsanity.com/paper/2312.09403/) (2023)

## Abstract (arXiv)

In this concise contribution, it is demonstrated that Recurrent Neural Networks (RNNs) based on Gated Recurrent Unit (GRU) architecture, possess the capability to learn the complex dynamics of rate-and-state friction (RSF) laws from synthetic data. The data employed for training the network is generated through the application of traditional RSF equations coupled with either the aging law or the slip law for state evolution. A novel aspect of this approach is the formulation of a loss function that explicitly accounts for the direct effect by means of automatic differentiation. It is found that the GRU-based RNNs effectively learns to predict changes in the friction coefficient resulting from velocity jumps (with and without noise in the target data), thereby showcasing the potential of machine learning models in capturing and simulating the physics of frictional processes. Current limitations and challenges are discussed.