# Forecasting the Forced van der Pol Equation with Frequent Phase Shifts Using Reservoir Computing

arXiv: https://arxiv.org/abs/2404.14651 · HTML: https://mlsanity.com/paper/2404.14651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 69 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 17 of 17)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Multi-Step Prediction of Dynamic Systems with Recurrent Neural Networks](https://mlsanity.com/paper/1806.00526/) (2018)
- [Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations](https://mlsanity.com/paper/2108.03561/) (2021)
- [Learning strange attractors with reservoir systems](https://mlsanity.com/paper/2108.05024/) (2021)
- [Reservoir Computing as a Tool for Climate Predictability Studies](https://mlsanity.com/paper/2103.06206/) (2021)
- [Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays](https://mlsanity.com/paper/2303.09042/) (2023)
- [Deep learning delay coordinate dynamics for chaotic attractors from partial observable data](https://mlsanity.com/paper/2211.11061/) (2022)
- [Reservoir Computing with Noise](https://mlsanity.com/paper/2303.00585/) (2023)
- [Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation](https://mlsanity.com/paper/1906.04059/) (2019)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [PyRCN: A Toolbox for Exploration and Application of Reservoir Computing Networks](https://mlsanity.com/paper/2103.04807/) (2021)
- [Delay Embedded Echo-State Network: A Predictor for Partially Observed Systems](https://mlsanity.com/paper/2211.05992/) (2022)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)
- [LSTM-based Anomaly Detection for Non-linear Dynamical System](https://mlsanity.com/paper/2006.03193/) (2020)

## Abstract (arXiv)

We tested the performance of reservoir computing (RC) in predicting the dynamics of a certain non-autonomous dynamical system. Specifically, we considered a van del Pol oscillator subjected to periodic external force with frequent phase shifts. The reservoir computer, which was trained and optimized with simulation data generated for a particular phase shift, was designed to predict the oscillation dynamics under periodic external forces with different phase shifts. The results suggest that if the training data have some complexity, it is possible to quantitatively predict the oscillation dynamics exposed to different phase shifts. The setting of this study was motivated by the problem of predicting the state of the circadian rhythm of shift workers and designing a better shift work schedule for each individual. Our results suggest that RC could be exploited for such applications.