Data-driven dynamic friction models based on Recurrent Neural Networks

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.