DR-RNN: A deep residual recurrent neural network for model reduction

TL;DR

This paper presents DR-RNN, a deep residual recurrent neural network designed for efficient model reduction of nonlinear dynamical systems, combining iterative residual minimization with deep learning for improved accuracy and stability.

Contribution

The paper introduces DR-RNN, a novel deep residual RNN architecture inspired by line search methods, for effective model reduction of complex nonlinear systems.

Findings

DR-RNN effectively emulates full order models with fewer parameters.

Combining DR-RNN with POD enhances model reduction for PDEs.

Deeper DR-RNN improves accuracy and stability.

Abstract

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual minimiser of numerically discretized differential equations. We formulate this iterative scheme as stacked recurrent neural network (RNN) embedded with the dynamical structure of the emulated differential equations. Numerical examples demonstrate that DR-RNN can effectively emulate the full order models of nonlinear physical systems with a significantly lower number of parameters in comparison to standard RNN architectures. Further, we combined DR-RNN with Proper Orthogonal Decomposition (POD) for model reduction of time dependent partial differential equations. The presented numerical results show the stability of proposed DR-RNN as an explicit reduced order technique. We also show significant gains in accuracy by increasing the depth of proposed DR-RNN similar to other applications of deep learning.