这篇论文用TAIR方法让神经网络学真实流体偏离理想气体的部分，超临界燃烧场景下误差降了数倍，做物理信息嵌入的可以看看。
该论文提出一种热力学启发的输入重参数化策略TAIR，用于超临界燃烧模拟中真实流体热力学性质的神经网络预测。TAIR将每个属性网络的原始焓坐标替换为目标匹配的热力学坐标：温度网络使用常cp理想气体混合物焓近似反推的温度估计，密度和压缩系数网络使用理想气体密度估计。在超临界甲烷-氧对冲火焰数据上，TAIR将温度T、密度ρ和压缩系数ψ的留出集RMSE分别降低约1.5、2.0和7.5倍。对于未见过的应变率火焰，对应因子达到3.6、14.5和6.0。目标不一致的交叉重参数化控制表现更差，证实增益来自热力学匹配的输入设计。
Thermodynamics-Informed Input Reparameterization for Neural Prediction of Real-Fluid Thermodynamic Properties in Supercritical Combustion
Real-fluid thermodynamic property evaluation is a major computational cost in supercritical combustion simulations. In the enthalpy-based pressure-correction formulation, the closure evaluates temperature T, density $ρ$, and compressibility coefficient $ψ$ from the solver state (h,p,Y) through enthalpy-temperature inversion and repeated real-fluid equation-of-state evaluations. Neural-network surrogates offer fixed-cost inference, but direct mapping from (h,p,Y) to $(T,ρ,ψ)$ must capture the enthalpy-temperature relation and non-ideal equation-of-state response, resulting in a complex regression problem. This work introduces a thermodynamics-informed input reparameterization strategy, termed target-aligned input reparameterization (TAIR). TAIR replaces the raw enthalpy coordinate of each property network with a target-matched thermodynamic coordinate: the temperature network uses a temperature estimate obtained by inverting a constant-$c_p$ ideal-gas mixture enthalpy approximation, whereas the density and compressibility networks use an ideal-gas density estimate. These algebraic transformations use only solver-available variables and species constants, guiding the networks to learn real-fluid departures from ideal-gas baselines rather than reconstructing the full closure from raw enthalpy. The method is assessed using supercritical methane-oxygen counterflow flame data against a raw-input baseline and target-inconsistent cross-reparameterization controls. TAIR reduces held-out RMSE by factors of about 1.5, 2.0, and 7.5 for T, $ρ$, and $ψ$, respectively. For an unseen strain-rate flame within the augmented thermodynamic envelope, the corresponding factors are 3.6, 14.5, and 6.0. The target-inconsistent controls perform worse, indicating that the gains arise from thermodynamically matched input design rather than generic preprocessing.