# Model-assisted deep learning of rare extreme events from partial observations

arXiv: https://arxiv.org/abs/2111.04857 · HTML: https://mlsanity.com/paper/2111.04857/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 4 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Analog forecasting of extreme-causing weather patterns using deep learning](https://mlsanity.com/paper/1907.11617/) (2019)
- [A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems](https://mlsanity.com/paper/1804.07240/) (2018)
- [Are extreme dissipation events predictable in turbulent fluid flows?](https://mlsanity.com/paper/1807.10263/) (2018)
- [An adjoint-based approach for finding invariant solutions of Navier-Stokes equations](https://mlsanity.com/paper/1508.06363/) (2015)
- [Using Machine Learning to predict extreme events in the H'enon map](https://mlsanity.com/paper/2002.10268/) (2020)
- [Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learning](https://mlsanity.com/paper/2107.08819/) (2021)
- [Data-driven prediction of multistable systems from sparse measurements](https://mlsanity.com/paper/2010.14706/) (2020)

## Built on by (most cited first, 3 of 3)

- [User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems](https://mlsanity.com/paper/2306.07526/) (2023)
- [Output-weighted and relative entropy loss functions for deep learning precursors of extreme events](https://mlsanity.com/paper/2112.00825/) (2021)
- [Dynamics-Informed Deep Learning for Predicting Extreme Events](https://mlsanity.com/paper/2603.10777/) (2026)

## Abstract (arXiv)

To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the training data is obtained from numerical simulations, as opposed to observations, with adequate samples from extreme events. However, to ensure the trained networks are applicable in practice, the training is not performed on the full simulation data; instead we only use a small subset of observable quantities which can be measured in practice. We investigate the feasibility of this model-assisted framework on three different dynamical systems (Rossler attractor, FitzHugh-Nagumo model, and a turbulent fluid flow) and three different deep neural network architectures (feedforward, long short-term memory, and reservoir computing). In each case, we study the prediction accuracy, robustness to noise, reproducibility under repeated training, and sensitivity to the type of input data. In particular, we find long short-term memory networks to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters.