# Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing

arXiv: https://arxiv.org/abs/2206.13336 · HTML: https://mlsanity.com/paper/2206.13336/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 81 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 30 of 44)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Supermasks in Superposition](https://mlsanity.com/paper/2006.14769/) (2020)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Learning to Remember: A Synaptic Plasticity Driven Framework for Continual Learning](https://mlsanity.com/paper/1904.03137/) (2019)
- [FearNet: Brain-Inspired Model for Incremental Learning](https://mlsanity.com/paper/1711.10563/) (2017)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Alleviating catastrophic forgetting using context-dependent gating and synaptic stabilization](https://mlsanity.com/paper/1802.01569/) (2018)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Memory Replay GANs: learning to generate images from new categories without forgetting](https://mlsanity.com/paper/1809.02058/) (2018)
- [Continual Learning in Generative Adversarial Nets](https://mlsanity.com/paper/1705.08395/) (2017)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [Why Neurons Have Thousands of Synapses, A Theory of Sequence Memory in Neocortex](https://mlsanity.com/paper/1511.00083/) (2015)
- [Selfless Sequential Learning](https://mlsanity.com/paper/1806.05421/) (2018)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)

## Built on by (most cited first, 6 of 6)

- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [A multifidelity approach to continual learning for physical systems](https://mlsanity.com/paper/2304.03894/) (2023)
- [Spatio-Temporal Fluid Dynamics Modeling via Physical-Awareness and Parameter Diffusion Guidance](https://mlsanity.com/paper/2403.13850/) (2024)
- [Decentralized digital twins of complex dynamical systems](https://mlsanity.com/paper/2207.12245/) (2022)
- [Data-Free Reservoir Features for Efficient Long-Horizon Cold-Start Continual Learning](https://mlsanity.com/paper/2606.27095/) (2026)
- [Continual Learning of Dynamical Systems in Recurrent Neural Networks through Recyclable Unit Gating](https://mlsanity.com/paper/2609.38356/) (2026)

## Abstract (arXiv)

Machine learning recently proved efficient in learning differential equations and dynamical systems from data. However, the data is commonly assumed to originate from a single never-changing system. In contrast, when modeling real-world dynamical processes, the data distribution often shifts due to changes in the underlying system dynamics. Continual learning of these processes aims to rapidly adapt to abrupt system changes without forgetting previous dynamical regimes. This work proposes an approach to continual learning based on reservoir computing, a state-of-the-art method for training recurrent neural networks on complex spatiotemporal dynamical systems. Reservoir computing fixes the recurrent network weights - hence these cannot be forgotten - and only updates linear projection heads to the output. We propose to train multiple competitive prediction heads concurrently. Inspired by neuroscience's predictive coding, only the most predictive heads activate, laterally inhibiting and thus protecting the inactive heads from forgetting induced by interfering parameter updates. We show that this multi-head reservoir minimizes interference and catastrophic forgetting on several dynamical systems, including the Van-der-Pol oscillator, the chaotic Lorenz attractor, and the high-dimensional Lorenz-96 weather model. Our results suggest that reservoir computing is a promising candidate framework for the continual learning of dynamical systems. We provide our code for data generation, method, and comparisons at urlhttps://github.com/leonardbereska/multiheadreservoir.