# Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows

arXiv: https://arxiv.org/abs/2104.01914 · HTML: https://mlsanity.com/paper/2104.01914/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 1 Apr 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [STEER: Simple Temporal Regularization For Neural ODEs](https://mlsanity.com/paper/2006.10711/) (2020)
- [Deep learning observables in computational fluid dynamics](https://mlsanity.com/paper/1903.03040/) (2019)
- [Fractional Deep Neural Network via Constrained Optimization](https://mlsanity.com/paper/2004.00719/) (2020)
- [Novel Deep neural networks for solving Bayesian statistical inverse](https://mlsanity.com/paper/2102.03974/) (2021)

## Built on by (most cited first, 6 of 6)

- [Learning stiff chemical kinetics using extended deep neural operators](https://mlsanity.com/paper/2302.12645/) (2023)
- [NINNs: Nudging Induced Neural Networks](https://mlsanity.com/paper/2203.07947/) (2022)
- [AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics](https://mlsanity.com/paper/2510.12999/) (2025)
- [A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Method](https://mlsanity.com/paper/2305.09842/) (2023)
- [Towards Foundation Models for the Industrial Forecasting of Chemical Kinetics](https://mlsanity.com/paper/2408.10720/) (2024)
- [Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics](https://mlsanity.com/paper/2512.14471/) (2025)

## Abstract (arXiv)

Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to the very large CPU requirements of chemical reactions (over 99%) a large number of flow and combustion problems are presently beyond the capabilities of even the largest supercomputers. Motivated by this, novel Deep Neural Networks (DNNs) are introduced to approximate stiff ODEs. Two approaches are compared, i.e., either learn the solution or the derivative of the solution to these ODEs. These DNNs are applied to multiple species and reactions common in chemically reacting flows. Experimental results show that it is helpful to account for the physical properties of species while designing DNNs. The proposed approach is shown to generalize well.