# Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computing

arXiv: https://arxiv.org/abs/2411.05867 · HTML: https://mlsanity.com/paper/2411.05867/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 12 of 12)

- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Parallel Machine Learning for Forecasting the Dynamics of Complex Networks](https://mlsanity.com/paper/2108.12129/) (2021)
- [An overview and comparative analysis of Recurrent Neural Networks for Short Term Load Forecasting](https://mlsanity.com/paper/1705.04378/) (2017)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling](https://mlsanity.com/paper/2202.07022/) (2022)
- [Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays](https://mlsanity.com/paper/2303.09042/) (2023)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Model-Size Reduction for Reservoir Computing by Concatenating Internal States Through Time](https://mlsanity.com/paper/2006.06218/) (2020)

## Built on by (most cited first, 1 of 1)

- [Dynamics-Informed Reservoir Computing with Visibility Graphs](https://mlsanity.com/paper/2507.19046/) (2025)

## Abstract (arXiv)

Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir computing with "expert" analytical models. Simulating the absence of an exact model, we first test the surrogate models with parameter errors in their expert model. Second, in a residual physics task, we assess their performance when their expert model lacks key non-linear coupling terms present in an extended ground-truth model. We focus on short-term forecasting across diverse dynamical regimes, evaluating the use of these surrogates for control applications. We show that hybrid reservoir computers generally outperform standard reservoir computers and exhibit greater robustness to parameter tuning. This advantage is less pronounced in the residual physics task. Notably, unlike standard reservoir computers, the performance of the hybrid does not degrade when crossing an observed spectral radius threshold. Furthermore, there is good performance for dynamical regimes not accessible to the expert model, demonstrating the contribution of the reservoir.