mlsanityData to 14 Oct 2026

AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics

arXiv 2510.12999 ↗First posted 15 Oct 2025cs.LG stat.MLcited by 2

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Abstract (arXiv)

Time integration of stiff systems is a primary source of computational cost in combustion, hypersonics, and other reactive transport systems. This stiffness can introduce time scales significantly smaller than those associated with other physical processes, requiring extremely small time steps in explicit schemes or computationally intensive implicit methods. Consequently, strategies to alleviate challenges posed by stiffness are important. While neural operators (DeepONets) can act as surrogates for stiff kinetics, a reliable operator learning strategy is required to appropriately account for differences in error between output variables and samples. Here, we develop AMORE, Adaptive Multi-Output Operator Network, a framework comprising an operator capable of predicting multiple outputs and adaptive loss functions ensuring reliable operator learning. The operator predicts all thermochemical states from given initial conditions. We propose two adaptive loss functions within the framework, considering each state variable's and sample's error to penalize the loss function. We designed the trunk to automatically satisfy Partition of Unity. To enforce unity mass-fraction constraint exactly, we propose an invertible analytical map that transforms the n-dimensional species mass-fraction vector into an (n-1)-dimensional space. We extend the proposed adaptive loss functions to trunk and branch training in two-step training of DeepONet with multiple outputs. We implemented another unity mass fraction constraint exactly using a softmax function on the predicted mass fraction. We demonstrate efficacy and applicability of our models through two examples: syngas (12 states), GRI-Mech 3.0 (24 active states out of 54). The proposed DeepONet will be a backbone for future CFD studies to accelerate turbulent combustion simulations. AMORE is a general framework, and here, we also demonstrate it for FNO.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 56 references that are in the map. First posted on arXiv 15 Oct 2025.

Builds on

27 of 56 references.

References · 27

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  4. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
  5. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  6. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  7. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  8. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  9. 2021Stiff Neural Ordinary Differential Equationscited by 78
  10. 2023Residual-based attention in physics-informed neural networkscited by 72
  11. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 67
  12. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
15 more
  1. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  2. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  3. 2023On the training and generalization of deep operator networkscited by 31
  4. 2023Learning stiff chemical kinetics using extended deep neural operatorscited by 30
  5. 2022On the influence of over-parameterization in manifold based surrogates and deep neural operatorscited by 29
  6. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  7. 2024State-space models are accurate and efficient neural operators for dynamical systemscited by 28
  8. 2021Partition of unity networks: deep hp-approximationcited by 16
  9. 2024Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architecturescited by 12
  10. 2024Learning the Hodgkin-Huxley Model with Operator Learning Techniquescited by 10
  11. 2024Ensemble and Mixture-of-Experts DeepONets For Operator Learningcited by 9
  12. 2021Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flowscited by 6
  13. 2024A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoringcited by 2
  14. 2025Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operatorscited by 2
  15. 2025Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)cited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kineticscited by 0
  2. 2026Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networkscited by 0