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 the 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, where DeepONet training is performed. We consider two-step training for DeepONet for multiple outputs and extend adaptive loss functions for trunk and branch training. We demonstrate the efficacy and applicability of our models through two examples: the syngas (12 states) and 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, in addition to DeepONet, we also demonstrate it for FNO.

翻译：刚性系统的时间积分是燃烧、高超声速流动及其他反应输运系统中计算成本的主要来源。这种刚性可能导致时间尺度显著小于其他物理过程相关的时间尺度，从而在显式格式中要求极小时步长，或需要计算密集的隐式方法。因此，缓解刚性带来的挑战具有重要意义。虽然神经算子（DeepONets）可作为刚性动力学的代理模型，但需要可靠的算子学习策略以恰当处理输出变量与样本间误差的差异。本文提出AMORE（自适应多输出算子网络），该框架包含一个能够预测多输出的算子以及确保可靠算子学习的自适应损失函数。该算子可根据给定初始条件预测所有热化学状态。我们在框架内提出了两种自适应损失函数，通过考虑每个状态变量及样本的误差对损失函数进行惩罚。我们设计了自动满足单位分解条件的干线网络。为精确满足质量分数总和为1的约束，我们提出了一种可逆解析映射，将$n$维组分质量分数向量变换至$(n-1)$维空间进行DeepONet训练。针对多输出DeepONet设计了两阶段训练策略，并将自适应损失函数扩展至干线与分支网络的训练。通过合成气（12个状态）和GRI-Mech 3.0（54个状态中24个活跃状态）两个案例验证了模型的有效性与适用性。所提出的DeepONet将成为未来CFD研究中加速湍流燃烧模拟的基础架构。AMORE是通用框架，本文除DeepONet外还展示了其在FNO上的应用。