# Reduced-space Gaussian Process Regression for data-driven probabilistic forecast of chaotic dynamical systems

@article{Wan2016ReducedspaceGP, title={Reduced-space Gaussian Process Regression for data-driven probabilistic forecast of chaotic dynamical systems}, author={Zhong Yi Wan and Themistoklis P. Sapsis}, journal={Physica D: Nonlinear Phenomena}, year={2016}, volume={345}, pages={40-55} }

## 29 Citations

### Data-driven nonintrusive reduced order modeling for dynamical systems with moving boundaries using Gaussian process regression

- MathematicsArXiv
- 2021

### Time Series Forecasting Using Manifold Learning

- Computer ScienceArXiv
- 2021

A three-tier numerical framework based on manifold learning for the forecasting of highdimensional time series is addressed and a comparison with the Principal Component Analysis algorithm as well as with the naive random walk model and the MVAR and GPR models trained and implemented directly in the high-dimensional space are provided.

### Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics.

- Computer ScienceChaos
- 2022

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the "curse of dimensionality" related to the training…

### Model-free forecasting of partially observable spatiotemporally chaotic systems

- Computer ScienceNeural Networks
- 2023

### Data-assisted reduced-order modeling of extreme events in complex dynamical systems

- Computer SciencePloS one
- 2018

A novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture is developed, showing that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone.

### Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

A data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks and a hybrid architecture, extending the LSTM with a mean stochastic model (MSM–L STM), is proposed to ensure convergence to the invariant measure.

### New perspectives for the prediction and statistical quantification of extreme events in high-dimensional dynamical systems

- PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

This article considers two classes of problems related to extreme events and nonlinear energy transfers, namely the derivation of precursors for the short-term prediction of extreme events, and the efficient sampling of random realizations for the fastest convergence of the probability density function in the tail region.

### Predicting observed and hidden extreme events in complex nonlinear dynamical systems with partial observations and short training time series.

- Environmental ScienceChaos
- 2020

A new mathematical framework of building suitable nonlinear approximate models is developed, which aims at predicting both the observed and hidden extreme events in complex nonlinear dynamical systems for short-, medium- and long-range forecasting using only short and partially observed training time series.

### Conditional Gaussian Nonlinear System: a Fast Preconditioner and a Cheap Surrogate Model For Complex Nonlinear Systems

- Computer ScienceChaos
- 2022

This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian nonlinear system (CGNS), as both a cheap surrogate model and a fast preconditioner for facilitating many computationally challenging tasks.

### Sequential Bayesian experimental design for estimation of extreme-event probability in stochastic input-to-response systems

- MathematicsComputer Methods in Applied Mechanics and Engineering
- 2022

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