mlsanityData to 7 Oct 2026

Learning stiff chemical kinetics using extended deep neural operators

arXiv 2302.12645 ↗First posted 23 Feb 2023physics.chem-ph cs.LGcited by 30

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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.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 12 of its 40 references that are in the map. First posted on arXiv 23 Feb 2023.

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12 of 40 references.

References · 12

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
  4. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  5. 2021Stiff Neural Ordinary Differential Equationscited by 77
  6. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  7. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  8. 2021Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functionscited by 49
  9. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  10. 2022On the influence of over-parameterization in manifold based surrogates and deep neural operatorscited by 29
  11. 2022How important are activation functions in regression and classification? A survey, performance comparison, and future directionscited by 29
  12. 2021Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flowscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 7; 2025: 12; 2026: 7.

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  1. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  2. 2023Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networkscited by 32
  3. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  4. 2024State-space models are accurate and efficient neural operators for dynamical systemscited by 27
  5. 2025Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEscited by 11
  6. 2024An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learningcited by 6
  7. 2024A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problemscited by 6
  8. 2024Neural Network Emulator for Atmospheric Chemical ODEcited by 5
  9. 2025BubbleOKAN: A Physics-Informed Interpretable Neural Operator for High-Frequency Bubble Dynamicscited by 5
  10. 2026FEKAN: Feature-Enriched Kolmogorov-Arnold Networkscited by 5
  11. 2025ChemKANs for Combustion Chemistry Modeling and Accelerationcited by 4
  12. 2023Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulationscited by 3
18 more
  1. 2025SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimationcited by 3
  2. 2024Geometry Matters: Benchmarking Scientific ML Approaches for Flow Prediction around Complex Geometriescited by 2
  3. 2025AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kineticscited by 2
  4. 2025Invertible Koopman neural operator for data-driven modeling of partial differential equationscited by 1
  5. 2026In Transformer We Trust? A Perspective on Transformer Architecture Failure Modescited by 1
  6. 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Modelcited by 1
  7. 2023Machine learning for advancing low-temperature plasma modeling and simulationcited by 0
  8. 2024Towards Foundation Models for the Industrial Forecasting of Chemical Kineticscited by 0
  9. 2025LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equationscited by 0
  10. 2025Enhanced accuracy through ensembling of randomly initialized auto-regressive models for time-dependent PDEscited by 0
  11. 2025Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecastingcited by 0
  12. 2025Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigmcited by 0
  13. 2025Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kineticscited by 0
  14. 2025PIP2 Net: Physics-informed Partition Penalty Deep Operator Networkcited by 0
  15. 2026Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networkscited by 0
  16. 2026Accelerating Bayesian inverse design in computational fluid dynamics using neural operatorscited by 0
  17. 2026Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solverscited by 0
  18. 2026Accelerating Chemical Kinetics for Exoplanet Atmospheres using Neural Networkscited by 0