# Reconstructing dynamics from sparse observations with no training on target system

arXiv: https://arxiv.org/abs/2410.21222 · HTML: https://mlsanity.com/paper/2410.21222/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 67 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [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)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [One Model to Synthesize Them All: Multi-contrast Multi-scale Transformer for Missing Data Imputation](https://mlsanity.com/paper/2204.13738/) (2022)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Machine-learning inference of fluid variables from data using reservoir computing](https://mlsanity.com/paper/1805.09917/) (2018)
- [Dynamical learning of dynamics](https://mlsanity.com/paper/1902.02875/) (2019)
- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation](https://mlsanity.com/paper/1906.04059/) (2019)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)

## Built on by (most cited first, 2 of 2)

- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems](https://mlsanity.com/paper/2506.19609/) (2025)

## Abstract (arXiv)

In applications, an anticipated situation is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed from the limited observations without any training data? This problem defies any known traditional methods of nonlinear time-series analysis as well as existing machine-learning methods that typically require extensive data from the target system for training. We address this challenge by developing a hybrid transformer and reservoir-computing machine-learning scheme. The key idea is that, for a complex and nonlinear target system, the training of the transformer can be conducted not using any data from the target system, but with essentially unlimited synthetic data from known chaotic systems. The trained transformer is then tested with the sparse data from the target system. The output of the transformer is further fed into a reservoir computer for predicting the long-term dynamics or the attractor of the target system. The power of the proposed hybrid machine-learning framework is demonstrated using a large number of prototypical nonlinear dynamical systems, with high reconstruction accuracy even when the available data is only 20% of that required to faithfully represent the dynamical behavior of the underlying system. The framework provides a paradigm of reconstructing complex and nonlinear dynamics in the extreme situation where training data does not exist and the observations are random and sparse.