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

arXiv: https://arxiv.org/abs/1709.00939 · HTML: https://mlsanity.com/paper/1709.00939/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2017.

## Built on by (most cited first, 20 of 20)

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- [Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs](https://mlsanity.com/paper/2202.12373/) (2022)
- [Active-learning-based non-intrusive Model Order Reduction](https://mlsanity.com/paper/2204.08523/) (2022)
- [A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detection](https://mlsanity.com/paper/2401.11860/) (2024)
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- [Phy-Taylor: Physics-Model-Based Deep Neural Networks](https://mlsanity.com/paper/2209.13511/) (2022)

## Abstract (arXiv)

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.