Learning a potential formulation for rate-and-state friction

TL;DR

This paper introduces a neural network-based potential formulation for rate-and-state friction laws, enabling more efficient implicit numerical simulations of interface slip in geophysics and engineering.

Contribution

It proposes a novel potential formulation using neural networks for rate-and-state friction, facilitating implicit discretization and computational efficiency.

Findings

Neural network potentials accurately emulate empirical rate-and-state friction.

The formulation enables implicit time discretization for efficient simulations.

Potential approach reduces computational cost of interface slip modeling.

Abstract

Empirical rate-and-state friction laws are widely used in geophysics and engineering to simulate interface slip. They postulate that the friction coefficient depends on the local slip rate and a state variable that reflects the history of slip. Depending on the parameters, rate-and-state friction can be either rate-strengthening, leading to steady slip, or rate-weakening, leading to unsteady stick-slip behavior modeling earthquakes. Rate-and-state friction does not have a potential or variational formulation, making implicit solution approaches difficult and implementation numerically expensive. In this work, we propose a potential formulation for the rate-and-state friction. We formulate the potentials as neural networks and train them so that the resulting behavior emulates the empirical rate-and-state friction. We show that this potential formulation enables implicit time discretization leading to efficient numerical implementation.