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

arXiv: https://arxiv.org/abs/2510.12999 · HTML: https://mlsanity.com/paper/2510.12999/

## 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 (most cited first, 27 of 27)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [On the training and generalization of deep operator networks](https://mlsanity.com/paper/2309.01020/) (2023)
- [Learning stiff chemical kinetics using extended deep neural operators](https://mlsanity.com/paper/2302.12645/) (2023)
- [On the influence of over-parameterization in manifold based surrogates and deep neural operators](https://mlsanity.com/paper/2203.05071/) (2022)
- [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)
- [Partition of unity networks: deep hp-approximation](https://mlsanity.com/paper/2101.11256/) (2021)
- [Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures](https://mlsanity.com/paper/2501.00016/) (2024)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [Ensemble and Mixture-of-Experts DeepONets For Operator Learning](https://mlsanity.com/paper/2405.11907/) (2024)
- [Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows](https://mlsanity.com/paper/2104.01914/) (2021)
- [A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoring](https://mlsanity.com/paper/2412.11967/) (2024)
- [Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators](https://mlsanity.com/paper/2505.14039/) (2025)
- [Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)](https://mlsanity.com/paper/2504.10720/) (2025)

## Built on by (most cited first, 2 of 2)

- [Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics](https://mlsanity.com/paper/2512.14471/) (2025)
- [Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks](https://mlsanity.com/paper/2605.04134/) (2026)

## 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.