# Thermodynamics-Informed Input Reparameterization for Neural Prediction of Real-Fluid Thermodynamic Properties in Supercritical Combustion

arXiv: https://arxiv.org/abs/2607.19241 · HTML: https://mlsanity.com/paper/2607.19241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Robust Large Margin Deep Neural Networks](https://mlsanity.com/paper/1605.08254/) (2016)
- [Acceleration of the NVT-flash calculation for multicomponent mixtures using deep neural network models](https://mlsanity.com/paper/1901.09380/) (2019)

## Abstract (arXiv)

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 psi 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,psi) 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-cp 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 psi, 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.