Gradient-Harmonizing-Based Deep Learning for Thermophysical Properties of Carbon Dioxide

Carbon dioxide presents many unique advantages for cooling and power cycles under supercritical or near-critical conditions, where the characterization of thermophysical properties is a daunting task. The present study proposes different deep feedforward neural network (DFNN) models for property evaluations of carbon dioxide. The all-in-one DFNN model appears acceptable for enthalpy, entropy, and thermal conductivity, but it exhibits poor performance in density, speed of sound, viscosity, and constant-pressure specific heat. The specific DFNN model presents limited improvement in the near-critical and pseudoboiling regions, where steep property gradients occur. To alleviate the situation, the sampling data are divided into easy samples and hard samples. Easy samples are data that have small-gradient norm and can be well fitted, whereas hard samples are those with large-gradient norms and are difficult to fit. The gradient-harmonizing method is proposed to solve the imbalance between hard and easy samples by rectifying their gradient contribution and assigning different weights. The resultant models show significantly improved performance as compared to the existing methods in the literature, with less than 0.4% in absolute average relative errors for the studied properties. The gradient-harmonizing algorithm can potentially be adopted to property evaluations of other substances involved in aerospace propulsion.