# Assessment of machine learning methods for state-to-state approaches

arXiv: https://arxiv.org/abs/2104.01042 · HTML: https://mlsanity.com/paper/2104.01042/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 63 references that are in the map.
- First posted on arXiv 2 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Caffe: Convolutional Architecture for Fast Feature Embedding](https://mlsanity.com/paper/1408.5093/) (2014)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [Orders-of-magnitude speedup in atmospheric chemistry modeling through neural network-based emulation](https://mlsanity.com/paper/1808.03874/) (2018)
- [Automated Fortran--C++ Bindings for Large-Scale Scientific Applications](https://mlsanity.com/paper/1904.02546/) (2019)
- [The Stabilized Explicit Variable-Load Solver with Machine Learning Acceleration for the Rapid Solution of Stiff Chemical Kinetics](https://mlsanity.com/paper/1905.09395/) (2019)

## Abstract (arXiv)

It is well known that numerical simulations of high-speed reacting flows, in the framework of state-to-state formulations, are the most detailed but also often prohibitively computationally expensive. In this work, we start to investigate the possibilities offered by the use of machine learning methods for state-to-state approaches to alleviate such burden. In this regard, several tasks have been identified. Firstly, we assessed the potential of state-of-the-art data-driven regression models based on machine learning to predict the relaxation source terms which appear in the right-hand side of the state-to-state Euler system of equations for a one-dimensional reacting flow of a N2/N binary mixture behind a plane shock wave. It is found that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, we investigated different strategies to speed-up our in-house state-to-state solver by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning methods into ordinary differential equations solvers may offer a speed-up of several orders of magnitude but some care should be paid for how and where such coupling is realized. Performances are found to be strongly dependent on the mutual nature of the interfaced codes. Finally, we aimed at inferring the full solution of the state-to-state Euler system of equations by means of a deep neural network completely by-passing the use of the state-to-state solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for these tasks.