## 3.5 Fundamental limits from chaos on instability time predictions in compact planetary systems

In the paper “Predicting the long-term stability of compact multiplanet systems” (Tamayo et al. 2020) an interesting approach to replace simulation runs by a machine learning algorithm.

Astrophysics is a science which has a long history of handling huge amount of data, no wonder that there are also ML applications in this field. This application helps to determine whether or not a planetary system will be stable. Until now the stability is determined by calculating an astonishing \(10^9\) orbits. Reducing simulation time by factor of 10,000 by combining analytical understanding of resonant dynamics in two-planet systems with machine learning was accomplished.

**Reducing simulation time:**

- Combine
- analytical understanding
- machine learning (XGBoost)
- calculation of only \(10^4\) orbits instead of 1\(0^9\)

The following graph shows the flow of computation and the utilization of machine learning to reduce the number of necessary simulations.

**Training the model:**

- simulate 100,000 initial conditions simulated
- 80% training set
- 20% test set
- machine learning (XGBoost)

### 3.5.1 Comparison between SPOCK and previous models

The comparison between SPOCK and previous models are shown below. At an FPR of 10%, SPOCK correctly classifies 85% of stable systems. According to the shown results SPOCK is a huge advance from previous models.

**Comparison between SPOCK and previous models:**

- At a false positive rate: 10%
- SPOCK has true positive rate: 85%
- N-body has true positive rate: 100%
- MEGNO, AMD, and Hill < 50%

with SPOCK being \(10^5\) faster than N-body

An explanation of ROC is given at chapter 7.6.1.1.1

### References

Hussain, Naireen, and Daniel Tamayo. 2020. “Fundamental Limits from Chaos on Instability Time Predictions in Compact Planetary Systems.” *Monthly Notices of the Royal Astronomical Society* 491 (4): 5258–67.

Tamayo, Daniel, Miles Cranmer, Samuel Hadden, Hanno Rein, Peter Battaglia, Alysa Obertas, Philip J Armitage, et al. 2020. “Predicting the Long-Term Stability of Compact Multiplanet Systems.” *Proceedings of the National Academy of Sciences* 117 (31): 18194–18205.