# Bilinear residual Neural Network for the identification and forecasting of dynamical systems

arXiv: https://arxiv.org/abs/1712.07003 · HTML: https://mlsanity.com/paper/1712.07003/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2017.

## Built on by (most cited first, 5 of 5)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Bridging observation, theory and numerical simulation of the ocean using Machine Learning](https://mlsanity.com/paper/2104.12506/) (2021)
- [State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics](https://mlsanity.com/paper/2107.11253/) (2021)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [Learning Runge-Kutta Integration Schemes for ODE Simulation and Identification](https://mlsanity.com/paper/2105.04999/) (2021)

## Abstract (arXiv)

Due to the increasing availability of large-scale observation and simulation datasets, data-driven representations arise as efficient and relevant computation representations of dynamical systems for a wide range of applications, where model-driven models based on ordinary differential equation remain the state-of-the-art approaches. In this work, we investigate neural networks (NN) as physically-sound data-driven representations of such systems. Reinterpreting Runge-Kutta methods as graphical models, we consider a residual NN architecture and introduce bilinear layers to embed non-linearities which are intrinsic features of dynamical systems. From numerical experiments for classic dynamical systems, we demonstrate the relevance of the proposed NN-based architecture both in terms of forecasting performance and model identification.