# Learning stiff chemical kinetics using extended deep neural operators

arXiv: https://arxiv.org/abs/2302.12645 · HTML: https://mlsanity.com/paper/2302.12645/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Learning two-phase microstructure evolution using neural operators and autoencoder architectures](https://mlsanity.com/paper/2204.07230/) (2022)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions](https://mlsanity.com/paper/2105.09513/) (2021)
- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [On the influence of over-parameterization in manifold based surrogates and deep neural operators](https://mlsanity.com/paper/2203.05071/) (2022)
- [How important are activation functions in regression and classification? A survey, performance comparison, and future directions](https://mlsanity.com/paper/2209.02681/) (2022)
- [Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows](https://mlsanity.com/paper/2104.01914/) (2021)

## Built on by (most cited first, 30 of 30)

- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2303.02243/) (2023)
- [RiemannONets: Interpretable Neural Operators for Riemann Problems](https://mlsanity.com/paper/2401.08886/) (2024)
- [State-space models are accurate and efficient neural operators for dynamical systems](https://mlsanity.com/paper/2409.03231/) (2024)
- [Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs](https://mlsanity.com/paper/2505.03595/) (2025)
- [An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning](https://mlsanity.com/paper/2408.13222/) (2024)
- [A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems](https://mlsanity.com/paper/2412.09009/) (2024)
- [Neural Network Emulator for Atmospheric Chemical ODE](https://mlsanity.com/paper/2408.01829/) (2024)
- [BubbleOKAN: A Physics-Informed Interpretable Neural Operator for High-Frequency Bubble Dynamics](https://mlsanity.com/paper/2508.03965/) (2025)
- [FEKAN: Feature-Enriched Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.16530/) (2026)
- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)
- [Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations](https://mlsanity.com/paper/2311.05961/) (2023)
- [Geometry Matters: Benchmarking Scientific ML Approaches for Flow Prediction around Complex Geometries](https://mlsanity.com/paper/2501.01453/) (2024)
- [SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimation](https://mlsanity.com/paper/2505.05625/) (2025)
- [AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics](https://mlsanity.com/paper/2510.12999/) (2025)
- [Invertible Koopman neural operator for data-driven modeling of partial differential equations](https://mlsanity.com/paper/2503.19717/) (2025)
- [In Transformer We Trust? A Perspective on Transformer Architecture Failure Modes](https://mlsanity.com/paper/2602.14318/) (2026)
- [GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Model](https://mlsanity.com/paper/2609.23761/) (2026)
- [Machine learning for advancing low-temperature plasma modeling and simulation](https://mlsanity.com/paper/2307.00131/) (2023)
- [Towards Foundation Models for the Industrial Forecasting of Chemical Kinetics](https://mlsanity.com/paper/2408.10720/) (2024)
- [LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equations](https://mlsanity.com/paper/2501.08423/) (2025)
- [Enhanced accuracy through ensembling of randomly initialized auto-regressive models for time-dependent PDEs](https://mlsanity.com/paper/2507.03863/) (2025)
- [Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecasting](https://mlsanity.com/paper/2510.00401/) (2025)
- [Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigm](https://mlsanity.com/paper/2511.06585/) (2025)
- [Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics](https://mlsanity.com/paper/2512.14471/) (2025)
- [PIP2 Net: Physics-informed Partition Penalty Deep Operator Network](https://mlsanity.com/paper/2512.15086/) (2025)
- [Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks](https://mlsanity.com/paper/2605.04134/) (2026)
- [Accelerating Bayesian inverse design in computational fluid dynamics using neural operators](https://mlsanity.com/paper/2605.26059/) (2026)
- [Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers](https://mlsanity.com/paper/2606.22150/) (2026)
- [Accelerating Chemical Kinetics for Exoplanet Atmospheres using Neural Networks](https://mlsanity.com/paper/2609.00428/) (2026)

## Abstract (arXiv)

We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with its extensions, such as the autoencoder-based DeepONet and the newly proposed Partition-of-Unity (PoU-) DeepONet to study a range of examples, including the ROBERS problem with three species, the POLLU problem with 25 species, pure kinetics of the syngas skeletal model for CO/H2 burning, which contains 11 species and 21 reactions and finally, a temporally developing planar CO/H2 jet flame (turbulent flame) using the same syngas mechanism. We have demonstrated the advantages of the proposed approach through these numerical examples. Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions. In the first case, we parametrize the initial conditions based on equivalence ratios and initial temperature values. In the second case, we perform a direct numerical simulation of a two-dimensional temporally developing CO/H2 jet flame. Then, we initialize the kinetic model by the thermochemical states visited by a subset of grid points at different time snapshots. Stiff problems are computationally expensive to solve with traditional stiff solvers. Thus, this work aims to develop a neural operator-based surrogate model to solve stiff chemical kinetics. The operator, once trained offline, can accurately integrate the thermochemical state for arbitrarily large time advancements, leading to significant computational gains compared to stiff integration schemes.